I disagree. The bottleneck is usually your eyes, not the monitor. On 1080p you can use small bitmap fonts that are legible even at low resolutions. 4K mostly gives you more flexible typography aesthetics, which doesn't improve programming productivity.
Too bad I can't bitmap-font UI elements. Being able to scale those freely (my DE allows it by a float value that is currently around 1,65) without too noticeable blur is my most important reason for a high resolution screen.
The by current standards normal sharpness is nice too (1080 screens aren't really blurry, they're pixely).
Eye resolution is ridiculously high. There's a reason companies started marketing 'retina' displays.
Small fonts will not always fall into discrete pixels which is especially true if the resolution is not very high. Which requires you to do antialiasing or mangle the characters.
Higher resolution displays allows you to render them more faithfully.
