Proof of Stake not only replicates the same dynamics that Bitcoin was designed to eliminate (more wealth -> more power in system) but also can only be made secure against a maximum of ⅓ byzantine actors, compared to Proof of Work's superior ½.
As for using it for Layer 1 systems, Andrew Poelstra nailed it in his conclusion [0]:
"We showed that by depending only on resources within the system, proof of stake cannot be used to form a distributed consensus, since it depends on the very history it is trying to form to enforce loss of value."
Proof of Stake might be useful at Layer 2 (becoming equivalent to voting stock in a company), but not as a base-layer consensus mechanism.
As for using it for Layer 1 systems, Andrew Poelstra nailed it in his conclusion [0]:
"We showed that by depending only on resources within the system, proof of stake cannot be used to form a distributed consensus, since it depends on the very history it is trying to form to enforce loss of value."
Proof of Stake might be useful at Layer 2 (becoming equivalent to voting stock in a company), but not as a base-layer consensus mechanism.
[0]: https://download.wpsoftware.net/bitcoin/pos.pdf