PoW is the ONLY consensus mechanism (that I know of) where separate blockchains compete for the SAME miners. This puts PoW in a class all by itself. What is the analysis if this is a good or bad thing?

If this is a good thing, the fact that PoW is the only consensus mechanism with such a property (ie separate chains compete for the same miners) - this makes dismissing certain projects out of hand much simpler.

The objective is P2P Cash. I am not sure if the same analysis applies for world computers or other objectives.

PoS coins whose coins are only valid within one chain doesn't have this property.

Proof of Storage - miners cannot jump chains because the setup process is extremely expensive (eg. plotting on Chia)

PoW has other amazing properties such as miners spend only the electricity that is financially viable. PoS coins if a whale has 10% of all coins, they can stake all of it regardless of what the marketcap of the coin is.

If PoW really is the best consensus algorithm - and the fact that BCH is the #2 PoW coin behind BTC - I would be extremely bullish on BCH. Its basically a given that BTC has taken itself out of the race for being digital cash....the field is wide open for BCH.