There is another model called DPoS (D=delegated) where you use your coins to vote for block producers, who then use their keys to sign blocks. It's pretty cool, because then the miners' (in DPoS known as "witnesses") keys need not directly control any coins (just sign blocks with the transactions of others).
For the most part, proof-of-stake has been strictly rejected as a viable means of building decentralized consensus by the industry experts.