Reinventing existing trust mechanisms but with an extra (computationally expensive) layer of things that can go wrong is the opposite of an improvement.

How would that work?

We have Yelp, Google reviews, Amazon reviews… how would something like that work on a blockchain/ledger and not be gamed just like the review systems we have now?

And how would we avoid this reputation blockchain from being populated by maliciously deceptive information, be it positive reputation promoted by the business through bribed or fake customers, or negative reputation promoted by unethical competitors?

I see no reason why a reputation system needs distributed consensus. It needs asymmetric encryption (signatures), but not a blockchain.