i'm always running out of the right size coin cell batteries

I wonder why they don't make NiMH rechargeable coin cell and button batteries, like they do AA and AAA batteries.

I wonder if it is because NiMH can't provide enough power in such a small form factor, or if one can't even make NiMH batteries in that form factor, or if both could be done but it just hasn't been done yet, or hasn't been mass produced for commercial sales.

I'm guessing it's the first reason (not enough power), since the non-rechargeable ones are Lithium.
Oh well.