Economics 101 says it does. Thats why the difficulty needs to increase as the hash rate increases
A non sequitur to be sure. You pointed out yourself that digital currencies are essentially infinite, so what scarcity is there? None. (modern) Money is not a tangible resource, it is only a medium of exchange. Scarce resources will find their price on a supply and demand curve. Money sharing the same "scarce" property distorts the ability to find a price. There simply needs to be enough money - a stable or targeted supply.