An 8x faster GPU with 10x faster memory bandwidth would handle the 4x increase in resolution, unless the extra power is used on bigger effects.
With the pixels being finer, they can reduce some things like anti-aliasing as well. For example on a regular PC monitor, you need LCD sub-pixel font rendering to make text look nice, but on a Retina resoution screen the pixels are so fine that you don't need sub-pixel fonts.
And that's the problem. PS4 is also has a GPU that's about 8x faster, with 7x higher memory bandwidth. And sure, it can run TloU at 1080p at mostly 60fps, yet the improved shadows are only available with 30fps lock. So 4K at 30fps should indeed be achievable, ie without any further enhancements.
Anti aliasing is already at a minimum in most console titles. Cheap solutions to reduce shimmer is about the most you get. You'll still need that at 4K.
Bigger effects will come first, otherwise people still without a 4K tv will literally see no difference. (Well I guess they'll be enjoying 4xFSAA by downsampling to 1080p)
I'm conflicted, I love a big screen with high resolution, yet I'm also eager to see some actual ray tracing used for realistic lighting, and VR needs 60 or even 75fps. 4k x2 @ 75fps ray traced VR games, not in 2020.