Which is actually done on commons, it just isn't very popular (on images, click the structured data tab and then look at depicts) [admittedly i think a big part of the problem is is implementation choices and UI decisions].
That's only "depicts" claims and is nowhere near comprehensive. It doesn't even come close to matching what's currently stated using categories. Running searches on that data is also hard compared to what IMSLP gives you for their own system.