At the current price I don't think it's really worth it, no. Really few games manage to take full advantage of 4K (Doom '16, as I mentioned, is one of them). Too many console ports with low texture resolutions and terrible optimizations these days. Older games will of course fare much better but the additional sharpness in the graphics is probably not worth the price of the hardware. For gaming I think 1440p and a high framerate are a better compromise at the moment.
That being said I have some trouble going back to my 1200p screens at work after being used to 4k at home. Surprisingly even for emacs and other work-related things 4K makes a pretty huge difference in my experience. Everything remains razor sharp even with a small font. I can split my screen and display a few full page datasheets and schematics alongside my code. No need to zoom in or anything. No aliasing, no pixels, I find it very relaxing.
Those hold up pretty well at 4K. In contrast I present to you Wolfenstein: The New Order which often looks very mediocre and yet manages to run worse than DOOM:
That being said I have some trouble going back to my 1200p screens at work after being used to 4k at home. Surprisingly even for emacs and other work-related things 4K makes a pretty huge difference in my experience. Everything remains razor sharp even with a small font. I can split my screen and display a few full page datasheets and schematics alongside my code. No need to zoom in or anything. No aliasing, no pixels, I find it very relaxing.