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That and button cells are designed to provide a low voltage for a long time but with very low current capability and are not really suited for 'dynamic' load currents.
So... you find them as backup batteries, in watches, flat remotes and toys.
Some are, some aren't. There are Lithium Ion rechargeable ones in a lot of the same sizes as the non-rechargeable ones. See LIR2032 and LIR2450 for examples. I don't know of any players using them though, and I agree about the small LiPo.