What resolution issues? UHD 4K is an exact pixel doubling (sic) of 1080p. For GPUs/games that can't handle 4K, run them at 1080p and get perfectly sharp images that fill your entire screen. This is way better than having stupid pillarboxing on an ultrawide monitor. As for performance, I run a $299 R9 280X. It runs modern RTSes super well on 4K.
I suppose it's kindof neat that 1080p divides evenly into 4K (3840 x 2160). That should give you a usable resolution for the several years it's going to be until the majority of games support that resolution. It'll also give you something to fall back on when your 280X can't pull off more 15fps (probably the majority of the time right now).
Besides, your line of argument has historically always been invalidated due to the rapid exponential growth of processing power. Right from "640k ought to be enough for anybody," anyone who has put forward this myopic argument has been wrong. GPU performance increases much much faster than screen pixel counts. A typical mainstream GPU costs much less than one of these displays. All in all, you are bound to upgrade your GPU much more frequently than your display. Spending more money for less pixels simply because your existing (and soon to be obsolete) GPU may not be able to handle it is an obviously stupid move.
It's interesting you mention "640k", because that was misquoted over 10 years later, and had nothing to do with processing power. The 4K resolution (3840 x 2160) is actually FOUR TIMES (4x) the number of pixels as 1080p virtually overnight. Yes, GPU power is always increasing, but nowhere near fast enough to cover that increase in requirements. New games also use more visual effects, which negates a moderate percentage of the GPU's generational gains. Current benchmarks show that if you want to consistently hit even 40fps at 3840 x 2160 with decent settings, you're going to need to spend a minimum of $800 for dual-290's or better. You're also going to need to regularly upgrade those (probably at least every 18 months), and take a beating each time.
I'm lost as to how that saves money over a $180-230 GPU every 2-3 years.