@mad-scientist
1. You can do this with a wrapped ETH token, or even better, wrapped staked-ETH token, today, no EIP required. rETH for example can migrate to a contract that supports this.
2. Adding this to ETH will mean a huge amount of trust in the code and math. Bugs may mean someone can mint free ETH, and we will have no way of knowing it. Unlike regular exploits, we may not know we've been hacked. Something similar happened with zcash (probably only by the good guys).
I'm not saying this is a bad idea, I am saying I would like to see it implemented on a token first, and probably formal verification in addition to bug-bounty and multiple audits.