TL;DR:
It's not about what a console can deliver as it is what a TV can display. Classic (pre digital) TV sets could only receive and display interlaced frames. So no sense in producing a non interlaced one.
Similar console developers would have been unwise to create consoles and content that could not be displayed on what Joe Aerage had as TV. Sales might not have been geat.
(In addition, therms like 480i or 480p are only defined in hindsight from a digital POV, and have only a restricted meaning when it comes to analogue TV)
In Detail
I was under the impression that "interlaced" video modes was only a thing for remote television content because it saved bandwidth to only send 50% of the data to the homes, so you could fit more TV channels in the same bandwidth (air or cable).
No. Well, not directly. Of course, everything in transmission is always about bandwidth, as that's the shared resource. But it wouldn't have been a big deal to double channel width in the early days.
Interlaced 50(60) Hz delivers 25(30) pictures full pictures per second. In theory more than enough for moving pictures s cinema does fine with 24 pictures per second. Except, TV works complete different from cinema. A cinema frame is displayed on the screen once and in al regions (almost) at the same time, but in TV a dot paints the picture line by line on the screen.
Doing this without any additional measure would result in a quite flickery picture, despite a frame rate equal or better than cinema.
The chain of thoughts looked a bit like this:
First stept: Make the screen disperse the beam energy over time (aka afterglow), so lit parts stay longer lit.
It should not stay lit too long, as that would make any motion blurr
With 25 (30) fps this would still result in an uneven, badly lit picture with a noticible fade (*1).
This is, BTW, the similar what makes pure 24 fps cinema flickery, like known from old silents. To reduce the inter frame flicker each frame later got displayed two or three times (*2) before moving to the next.
Drawing a revived picture twice would have worked as great on TV, except a CRT got no storage, so it had to be send more often than 25(30) times per second
Thus doubling the transmitted frame rate was the way to go.
Doubling allowed to reduce the persistence allowing to reduce blur
Doubling improved fast motion as well
So far a nice solution. A picture with 200-300 horizontal lines is quite fine for TV and would satisfy all needs. Producing TV content at 50(60) Hz frames would have been no issue. But then there were movies. They were produced on 24 Hz, so transmitting every picture twice would work quite as good as genuine TV production, but waste about half the bandwidth.
Adding interlace allowed to increase resolution without increasing bandwidth.
Thanks to the wonders of human sight movies now used the 50(60) fps to display their 24 fps in higher resolution, while genuine TV content got real 50 (60) fps in kind o an enhanced resolution.
I thought that all video games, being local to the customer's home with a video cable between the console and the TV, used "progressive" mode, meaning "not interlaced", since there was a dedicated video cable between the two units. Why would it have to send "half the data" in that scenario?
Because that's what the TV set expects as input and is able to display. A (classic, CRT) TV set does not combine two 'half' pictures into a single one to be displayed at double fps, but displays each 'half' on it's own, the second offset by a line. It's the way a CRT hardware works.
But then I watched a video on YouTube where it was casually mentioned that some games used "480i" instead of "480p", without further explaining it. Apparently, this was done very late, so it was not some kind of early 1980 video game console technique either.
Because games need to be compatible to the TV hardware (and standards) out in the field. It's not a great idea to produce a console that is can only work with the very latest displays - at least not if one intends to sell more than a few.
I assume that the picture must suffer in some subtle way from this "only every other line of image data", but it must be far more noticeable for video game content compared to a movie or TV show.
Not really, rather the other way around, as a console game is able to adjust. Keep in mind, 480i or 480p does only tell part of the story, as that number only names a frame size and structure, not the frame rate. Interlaced will usually create 50 (60) fps, while the same as progressive can be 25 (30) or 50(60) fps.
A classic TV set expects 50(60) 'half'-frames per second, so a console can use this as
- 50 frames per second with 'half' vertical resolution, or
- 25 frames per second with 'full' vertical resolution.
So any game that is about fast action, like a race game or a (complex) shooter will create each frame separate and get a smooth 50(60) fps with at cost of some resolution (288/240 horizonal). In contrast a game that is more about beautiful pictures, or lots of content may go ahead and do 25(30) 'full' frames using full 576 (480) horizontal lines (*3).
Oh, and of course games could go ahead and do fast content with high resolution - with the same drawback as TV content had with motion artefacts.
*1 - Yes, that is in fact related to the wandering dark bar that is visible when an unsynchronized camera films a CRT TV.
*2 - Or more exact, the douser that covers the film movement between frames also cuts one (two) more times within a frame, transposing the flicker to 48 or 72 Hz, where it gets way less noticible.
*3 - In reality this wasn't uses as often due memory limitations to generate and hold pictures that large.