You won’t be able to do ultra, but you can do high at 1080p30fps in most every modern game pretty easily for that price. 1080p 60fps for a solid chunk of them too.
https://ca.pcpartpicker.com/list/MzFVh3
https://m.youtube.com/watch?v=A6coMhaOw0Q
Your point still stands though; you’re still better off spending 1000$ so that you don’t end up shooting yourself in the foot with regards to upgradeability, which is one of the big reasons people want a PC in the first place.
They exist, but they’re not nearly as fleshed out as the bitcoin vanity generators are. https://github.com/danielewood/vanityssh-go