Wouldn't it be better to increase PPI instead of monitor size?
I mean, less need for AA, less noticeable dead/stuck pixels, more desk space...
Depends. Keeping the physical size of the monitor the same but increasing the resolution (and also increasing the pixel density at the same time) is fine with some applications but can be a pain with others. OS X is generally much better at handling it on an OS wide level but although Windows 10 has better DPI scaling it's still on an application, by application basis. And most of what I used day to day fucks up something horribly to the extent it's detrimental to accuracy.
Though if you want to have a monitor where you shouldn't be able to perceive individual pixels you'd probably need something in the region of 5120x2880 at 27ish" from a desk distance of about a foot. And even then that still on it's own isn't going to solve all the aliasing issues games themselves might have.