Unfortunately, you can simply change the market cap by choosing different exchanges...
Just the difference from Coinbase and Bitfinex right now would make the market cap swing by 600 million.
Really useless metric, especially since it is obvious some coins will never be sols as they are lost forever.
I've always wondered why in the world do exchanges put that metric anyway.
So it shows basically nothing important for us users
About OP's question - I think the market works in other way. People decide what price is fair for things (especially when it comes to currencies).
The more people want it - the higher price basically.
Person who buys BTC for 95k will wait until he can sell it for 105k. And all that time while he waits - more people wants bitcoin and price goes up (or the opposite way if BTC lacks popularity)