"Market cap" is borrowed from equity - the market cap of Apple for instance is determined by the number of shares of Apple outstanding x their price. But those shares have intrinsic value in that they grant you rights to a proportional amount of Apple's cash flow. If you were to destroy 50% of Apple's shares, the remaining half would be worth twice as much since the present value of Apple's cash flows hasn't changed.

Assets and currencies don't have market caps in any sense. Take a look back pre-Bitcoin and there are basically no references to the "market cap of Gold" or any such thing, they've all arisen due to the comparisons to Bitcoin. There's no intrinsic or underlying value, prices are purely trade driven. This doesn't make them "bad" per se, just completely different than something like Market Cap can capture.

As one other point for Bitcoin specifically, basically nobody knows how many Bitcoin are actually in circulation. There are a million+ lost / inactive. If someone moved a single BTC out of Satoshi's wallet, the price would very likely collapse nearly instantaneously. So how can a "market cap" be treated seriously if a single "share" trading hands at current market prices would collapse it. Bezos sells over $1 Billion of Amazon stock per year to no impact on AMZN.