1280x1024@24-bit fits in 4 MiB. Why wouldn't you take extra screen space?
Keep in mind that games didn't usually run in 1280x1024 at the time. Back before LCDs became the dominating screen technology, you didn't care about the "native resolution" of the display - you didn't get the ugly "one pixel is stretched over two physical pixels, its neighbour only has one physical pixel". Even modern LCDs tend to look awful at their non-native resolutions (not helped by the use of sub-pixel rendering of fonts etc.), but the same thing wasn't true with CRTs.
So you had your workstation running 1280x1024, giving you the most of your 4 MiB graphics card. And when you wanted to play a game, it switched the resolution to something like 800x600 or 1024x768. The image was just as clear in both cases, you didn't get any weird aliasing or sizing artifacts.
This changed when LCDs came around; native resolution is a big deal on LCDs. Running a 800x600 game on an 1280x1024 LCD (of the time, though many quality issues remain to this day) will result in many artifacts. But here's the thing - LCDs weren't for games. No gamer would ever voluntarily use an LCD - they were designed for office use (and of course, portable computers - but that's a whole another can of worms). They had poor colours, poor response times, bad aliasing issues and couldn't adapt to other resolutions well. It made perfect sense to give the most screen space possible, which with the (then rather standard) 4 MiB graphics cards was 1280x1024@24-bit (while also giving nice fallback to 16-bit and 8-bit for smaller VRAM).
It took many years for LCDs to become mainstream even among gamers (mostly because of their convenience - size, weight, cost etc.). By then, 1280x1024 was already the standard, and most importantly, games became largely aspect ratio agnostic anyway. The next big jump had to wait for people watching movies on their computers, which helped the move to 16:9 and 16:10 (for that handy extra bit of vertical space).
Of course, there are other possible options that have pretty much the same benefits (or take other trade-offs). In the end, it's just that one of those dominated the others. Following the leader is often a good idea, since it makes it easier to reach a bigger portion of the market.