4000hz does work properly with mice.
But it's indeed unnecessary/useless, unless you have that quantum reflexes with your 500hz monitor with your 500fps+ compatible game.
I think just about every 4000Hz mouse pzogel has reviewed here has instability at 4000Hz.
The competitive edge it provides is - like you say - "unnecessary/useless" but the jitters and inconsistent input caused by polling instability is a very real and very noticeable drawback that will absolutely, 100% cause you to miss your shot, lose the match, and get pissed off with the stupid hardware that cannot do what it claims.
Most people who want high-refresh gaming have 240Hz displays or slower. 144-180Hz appears to be the sweet spot. The 300/360/500Hz panels are ludicriously niche and come with a mountain of significant drawbacks, but even on a 300Hz panel, you're getting at least 3 samples per frame at 1000Hz polling which is already overkill by at least a factor of 2!