In this vein; you can also get a lot of mileage out of boring off-lease corpo boxes.
Not quite as easy as it used to be; since more of them are laptops or various USFF desktops that are not meaningfully expandable; but if you can get something in mini-tower(or, if you don’t mind the somewhat higher power draw, something that was originally sold as ‘workstation’, that will also be much more likely to have a PSU that can just take having a proper GPU slapped in).
Most, though not all, games are more GPU than CPU bound when it comes to getting good-enough performance out of them; and the OEMs that do corporate box pushing tend to try to sell you on a little more CPU than your case probably actually needs; and their customers often don’t have too much incentive to push back because buying 1000 of the same thing and being able to deploy it to anyone is significantly less admin overhead than slicing and dicing and being stuck having to ensure that the i3s only get assigned to light duty systems, i5s for middleweight standard use, and i7 for those business analysts who hit the Excel real hard.
Such systems will probably have some proprietary bullshit(whether it be relatively minor like the front-panel header; or a potential dealbreaker like a completely nonstandard motherboard PSU connector); but they are available for a pittance, mostly low on nasty quirks, aside from specific proprietary parts that are identifiable up-front, and tend to be lacking purely in the GPU department.
One thing to watch out for, though, is vendors trying to take advantage of the relatively long period of Intel not reshuffling their high-level marketing terms. “Core i3/i5/i7” has been used for 14 generations of parts, starting with Nehalem in late 2008 and running to the present(the new thing is "Core 3/5/7 or Core Ultra; but so far that’s only mobile; not sure when the desktop parts using it will show up); so if someone just says Core i7!!! they could be talking about a decade-old Broadwell part and not technically be lying. Anyone worth thinking about giving money to will, of course, supply an actual model number; but you do have to check.
