I found one document which might shed some light why 192 lines was used before 200 caught on.
The TI 99/4 used a TI TMS9918 VDP, which based on the document, was designed as a chip for simple low cost systems, i.e. a chip for early home computers. It was allegedly a chip with highest resolution full color capability of any single chip systems of it's time. It claims that the resolution is near the limit for ordinary color television, being the highest practical for home computers used with ordinary TVs.
It does acknowledge that Motorola MC6847 offers higher resolution but says it trades colour variety with higher resolution.
So the 192 lines offers 24 rows of text with font height of 8 pixels. Now for example C64 offered both 24 and 25 text rows, so the extra 8 scanlines to get up to 200 scanlines and 25 text rows may not sound like much more complex.
In reality, the compexity might grow. For example in graphics mode, the TI VDP splits the screen into three 64-line sections adding up to 192 lines, and each 256x64 section uses 256 tiles of 8x8 pixels, so three separate 256 tile maps are used.
As 64 is a power of 2, it likely made things much easier to detect overflow from 63 to 0, and jump to next section, than to compare with some other number. And a reason why all sections are identical and add only up to 192 scanlines.
How it all works with NTSC lines is a bit difficult to assess, as many chips tend to invent their own line numbering scheme.
NTSC starts line numbering from 1 after last non-blanked line, with the first blanked line in vertical blank area. There are 3 blank lines with equalizing pulses, 3 sync lines, 3 blank lines with equalizing pulses, and 11 standard blank lines. That's 20 total blank lines, with lines 21 through line 262.5 active, so 241.5 active lines. 21 is generally reserved for closed captioning and we can ignore the half line, so that's 240 lines of video sent. So generally, lines 21 and 262 would not be visible any more. Earlier on, the blanking was shorter and 486 interlaced lines was possible, or 243 per field.
As the TI VDP uses 262 total lines, not 262.5 which means progressive.
Going through in same order, there are 3 blank lines, 3 sync lines, and 13 blank lines. So 19 total blank lines. Then there's 27 lines of top border, 192 lines of actual screen data, and 24 bottom border lines. So active video data sent on 243 lines.
If we simplify things a bit and make some assumptions, in NTSC the center of the screen is halfway between active image lines of 120 and 121, or roughly 120.5 lines before the end of frame.
With TI VDP, the halfway of the 192-line screen is between lines 96 and 97, so there is 96 lines plus 24 bottom border lines, or 120.5 lines. The center of the screen matches assumed center of standard NTSC transmission.
If I find timings for other platforms, I will add them. NTSC details for C64 are much harder to find than PAL.