It doesn't seem to me that bitcoin's "the hashiest chain wins" approach is "broken", so maybe we should refrain from "fixing" it.
I think the main point is that no scheme can prevent a complete reversal from the genesis block. If you have 2 chains that fork at the genesis block, then you can only compare the total POW.
However, if they fork at a later point, you could use something like proof of stake. or burn or whatever. Only stakes from before the fork would count though.
If the coin value before the fork is distributed, then this distributed checkpointing.