Consensus protocols such as those of Tendermint, Red Belly Blockchain or Algorand can be of great help when dealing with the problem of Finney attacks, and similar sorts of abusing of excessive 'thing' power, give a particular 'Proof-of-Thing', among other solutions.
So far, as far as I know, these protocols have only been proposed for private/consortium blockchains, or at least when it refers to users that can append blocks, (and sometimes users who can choose on the permission of other users).
This can be, depending on the view, considered as a disadvantage as big as the possibility of attacking blockchains based on Proof-of-** by owning enough relative resources in the network.
My question is: has any of the above-mentioned consensus protocols, or any other that follows a similar consensus approach, been seriously considered for public blockchains? are there existing implementations running?