Not really. There is an end point. Also, resolution is not free, this is a tradeoff, when you push more pixels on screen it means more work for the GPU (or CPU in some cases) and more loading time and space to load all those high-dpi resources...

At this point I clearly prefer lower latency and higher framerate over more pixels.

Sure, to a point. But the step-up in question here (1080p to 4K, at sizes like 15–27″) has clearly visible benefits.

And sure, resolution isn’t free, but at these levels that was an argument for the hardware of eight years ago, not the hardware of today. All modern hardware can cope with at least one 4K display with perfect equanimity. Excluding games (which you can continue to run at the lower resolutions if necessary), almost no software will be measurably affected in latency or frame rate by being bumped from 1080p to 4K. Graphics memory requirements will be increased to as much as 4×, but that’s typically not a problem.

When my monitors die (they are already 12 years old) I'll switch to 120Hz or more, but I am still not convinced by the high-dpi monitors I've tried.

Also, I don't like using non-integer resolution scaling, the results are always a bit blurry/unpleasant, even on high-dpi monitors.

That's true, undeniably. But I think the better tradeoff still is to go up in size: IMO the optimal monitor size is 38". Big enough, but not too much head turning. Would I get a sharper 38" if possible? Sure. But I wouldn't compromise on size to gain higher DPI.