It's absolutely still possible, but note that screen resolution has increased much faster than CPU speed - if you want software-rendered 320x240 like Quake II,

It's absolutely still possible, but note that screen resolution has increased much faster than CPU speed - if you want software-rendered 320x240 like Quake II, or even 1024x768, you'll probably be OK, but if you want to go to full HD even modern CPUs will struggle, and 4K or higher is right out. A common solution is to make a low-resolution texture (like 800x480), draw onto it with a software renderer, then use hardware rendering to scale it up to full-screen. You can even add filtering like faux scanlines or a convex CRT effect.