I guess the reason why bitcoin has a stable price is because miners are mining sometimes or even stop mining at all. The supply of coins freeze and the price would definitely freeze to. Correct me if im wrong but i really believe mining and the price are linked. If one stop moving then the other one will follow.
I already heard such statements going around about the relationship between price and bitcoin mining. It says that for miners to be able to profit or at least breaks even the price should be around $6K but I'm not sure if this theory sounds plausible though. Did miners pump the price if bitcoin goes below $6K, or it is the whales who really pump the price and doesn't want to get it below $6K?
Unless though we have definite proof about the price relationship, this is just another theory and be included in the mysteries surrounding this crypto sphere.