From https://en.wikipedia.org/wiki/BBC_Micro "the height of the graphics display was reduced to 200 scan lines to suit NTSC TVs". But NTSC is supposed to have 241 visible scan lines per half frame. Why wouldn't you want to make the graphics display vertical resolution 240 instead of 200?
While nominally 241 scan lines were visible in the sense they contained video information, all TV sets hid a varying amount of scan lines on top and bottom (and left and right) by overscan and by the bezel in front of the screen.
So with a vertical resolution of 240, on most TV sets parts at the top and bottom would not be seen. While this doesn't matter much for movies, it's not a good thing if you want to do text editing.
This is also the reason while basically all homecomputers and game consoles had some sort of border (which often could be colored) around the center part of the image that carried information: It was to make sure this central part would be visible on all TV sets.
No, NTSC does not have 240 (or 241, or 243, or whatever other similar figure a particular source might state) visible scanlines. It has 240 active scanlines. This includes a fair bit of overscan, to allow for both some variation in the analogue camera and the analogue receiver, so that the viewer sees a seemingly continuous picture all the way to the visible edge of their tube without any of the spurious studio paraphenalia that may sneak into the edge of shot momentarily until the camera operator corrects for it, weird glitches due to nearby sync pulses and so-on.
You may notice that a VCR, DVD player, or games console (particularly a later model) which is designed to give a fully overscanned image will claim to output 240 (or 480) lines, or something close to that, but there are a great number of home computers, and indeed earlier consoles, which instead output something closer to 200. The lower end like the VIC20 run maybe 184, the majority are 192 or 200 (or double up to it from 96 or 100), and a few push the boat out to maybe 212 (the MSX2 range, for example) or 216, which is pretty much the theoretical max that can be just about seen on a good majority of sets.
This is because they are made not only as screen-filling graphical entertainment devices where a little bit of detail lost at the edges is unimportant, but as general purpose machines where a good portion of user interaction is through text, or detailed on-screen diagrams, which you ideally want all, or certainly a good 99% of to be clearly visible. There's no point going to the programming and processing trouble of generating and rendering that text or graphic to the screen if no-one's going to see it, and the memory and/or effort that would go towards provisioning the extra lines is a waste that could be used to improve the rather less fixed/prescribed horizontal resolution, or the colour depth, or just storing additional character definitions and program data.
Some others straddle the line with 220 or 224, which is generally enough to achieve overscan on most NTSC TVs without bothering to generate the extra 16 lines that no-one will ever see. They can however generally be considered cousins of the 240-line models, and for the same reasons.
In general these modes persist in PAL-land, largely through inertia, laziness/ignorance, and economics, as well as compatibility reasons. If you're going to make a certain design of machine that will, hopefully, become as popular as possible and have global reach, you don't want the software causing problems in different parts of the world because the screen resolutions don't match (and depending on the program it can be as trouble some to have too many lines, as not enough). So you fix the screen mode to be the same everywhere... and just set up the video hardware to have an extra 50 lines of blanking in the PAL models vs the NTSC ones. In most cases this just means the Euros get slightly annoying but workable letterbox-o-vision with about 10% of the screen both above and below the active image being a flat border instead of containing useful imagery that extends almost to the screen edge; in some, ironically often those which have hardwired regional lockouts which you'd think would be partly aimed at providing fully localised and resolution-adapted versions of NTSC software, it can be a bit more troublesome where the generated image runs almost all the way to the edges but has loads of visual garbage along each edge...
Except in a few very limited cases, which tend to have suffered their own daft compatibility issues. Firstly the BBC Micro, which defaults to 256 lines in its original PAL incarnation; this is about as good a fit for our screens as the 212-line MSX2 display is for NTSC... that is, with an optimally calibrated screen, it's pretty much a perfect maximum. 240 lines would be a more logical equivalent, given the ratios of active linecount and the framerate vs linerate relationships, and appear about as tall as 200-line on NTSC, but I guess the draw of that perfect binary alignment is just too much, as we see 256 rather more often. Anyway, though 200-line is an entirely routine, official alternative mode (all of the regular 256 modes have a 200 counterpart, perhaps with a mind towards globalisation or just using a 60Hz monitor for less flicker, perhaps to make porting software from lower resolution rivals and predecessors easier), enough native software was made to run strictly in 256 mode that it probably caused a good deal of headaches trying to localise and market it for e.g. the US market, and is a pointer for why it didn't ever take off there. That and it was essentially stepping on the toes of both the Apple ][ and the Atari 8-bits, both 6502 based machines of, clock speed aside, rather similar capabilities and expandability... and domestically produced to boot.
Similar to that, the Amstrad PCW. Its green screen and high resolution gave an impression of something similar to the IBM MDA, or - thanks to the graphics - a Hercules Mono card. Actually it was just a CPC with tweaked firmware and the guts of a regular B/W TV, calibrated for a slightly smaller scan than usual (so 720x256 at the regular clock rate would still fit with a fair bit of underscan) and mated to a long-persistence green phosphor tube. For reasons known only to Alan Sugar, when exported to the states, it too defaulted to the optional 200-line/60Hz mode despite the screen being built-in and looking perfectly fine at 256/50, considerably reducing how many rows of text / cells you could fit on-screen with the word processor and spreadsheet programs, and breaking compatibility with pretty much every single other program, especially the games, ever made for the platform. At least in that case it was just a software command to switch it back before retrying...
Then the Amiga, which is a bit of an odd fish given that it's a US product, the PAL mode seems to almost be an afterthought (and the flicker, especially in interlace, was enough to make 60Hz modeswitch utilities fairly common), but it then ended up becoming more popular in, and being heavily programmed for in Euroland than its actual home. Some softies just went with the ROM-default 256-line mode and then had their programs fall down hard on NTSC machines because they can't even set that as a deep-overscan mode (unless they're first tripped into PAL mode somehow, by hardware tweaks or clever software), topping out instead at about 243 lines, and the alternative of 128 lines doubled up by interlace just looks horrific. A rare few made dual 200 and 256 line versions of their programs. And the rest just threw in the towel and defaulted to plain 200-line mode for wider compatibility, or maybe just through laziness as that (or 192-line) was what the original/most other versions of the game they were porting TO the Amiga used, so why rock the boat and end up spending ages redrawing all the graphics from scratch? The problem with that being ... they rarely bothered checking for a PAL machine, and offering the option either of attempting to force it into 60Hz mode (which generally looked better because of the corrected aspect ratio and reduced eyestrain), or staying at 50Hz but with properly adjusted borders so the image was squashed but centred. Instead they just ran with the defaults, and the picture therefore clamped itself to the top of the screen, and had the lower 20 to 25 percent blanked out with border colour. Jeez. (If you had something like the quite widely adjustable Philips CM8833 or Commie 1084 monitor, it wasn't so bad, as you could stretch and reposition, but on a TV or simpler monitor you were stuck). And that's before considering the oddities of things like DblPAL mode promotion on later machines...
And finally, if memory serves, the Playstation and PS2... which could go up to 256p or 512i in PAL regions, but precious few titles ever went beyond 240/480 or even the more common 224/448 or 216/432. I think TOCA Touring Cars was amongst them, which makes sense for a UK-developed game. Even the otherwise reasonably well adapted Gran Turismo and SSX series seemed to have a hint of a letterbox border, presumably running 240 line, just slightly breaking their otherwise pretty decent immersion. (GT4 on the PS2 actually reveals their CRT, as well as NTSC focus/prejudice; if you hook the machine up over component cables to get 1080i HD output, there's a clear border around the image on an LCD, where the resolution has been trimmed a bit to keep the framerate up, possibly to 1024i, maybe even 960, but would likely not be visible on a hi-def CRT with the same degree of overscan as a standard def model...)
FWIW: PAL does not have 288 / 576 (or whatever) "visible" lines either. As per the above, you get about 256. Some sets maybe only low 250s, maybe 252, but unlikely to be even as low as 240. Probably some you might nudge into the 260s. But the only time I can push my A600's interlace overscan past 560 lines (or, indeed, the horizontal overscan up past 350/700 pixels) is if it's connected to that same minimal-overscan LCD as per other examples above. On a regular CRT it's barely worth playing with the settings, as the default 320/640 x 256/512 more or less completely fills the visible area already (and, if you use a 60Hz switch, the default 200/400 lines are only a little bit shorter; you could maybe add another 20 through overscan mode at the most)