Their value is so volatile because they have no intrinsic value, no government (that I am aware of) is demanding tax paid in a cryptocoin. There is also no mechanism for increasing the value of the coin, through a central bank interest rate. There's also no means to increase the supply (after mining runs out) to allow for economic expansion, eventually you will end up with run away inflation, with no mechanism to control it. Honestly they don't work as currencies, they are speculative assets underpinned by some interesting but largely redundant technology.

Proof of stake is built on trust, much like the financial system, so why reinvent the wheel for a corruptible ledger of a non-trustless, non-currency?