Such a proposal was raised on ethresear.ch in July 2018, and is still under active discussion.
https://ethresear.ch/t/first-and-second-price-auctions-and-improved-transaction-fee-markets/2410
Why isn't this already implemented?
Firstly, it'd require a hard fork. (No big deal; it could go in with the next scheduled network upgrade.)
Secondly, you're changing the incentive system and therefore the cryptoeconomics at play. The current system works and is well understood from a game theory perspective. Changing things would presumably first require drawn-out academic discussion on how best to design an implementation. We're just not there yet.