doublespend – If there was an easy way to check for double spends, will consensus algorithms be needed?

Currently, checking for double spends is very computationally expensive, so consensus algorithms, like POW, were put in place to more easily prevent double spends among other things.

Ignoring the fact that a consensus algorithms allows for other essential things to be done, like making sure that new cryptocurrency can only be mined at a fixed rate; if there was a way to very efficiently detect double spends in an incoming blockchain and the protocol was changed so it will reject a blockchain that has double spends and it will accept accept a blockchain with no detected double spends, then will there be no need for consensus algorithms?