Omitting information is a pretty serious attack in a reputation based system. It would be like if all 1 star reviews on a product are omitted. You can have multiple hosts but then its on the viewer to find and verify on other hosts. And there is no garentee a history will continue to be hosted long term. Likley many histories will be lost over time. Especially considering these hosts then need a profit motive or some other motive to continue hosting them. You can have chains of signatures together similar to how SSL certs work but you will still need an authority at the end of that chain and it would result in many versions of the chain as multiple entities interact with it.

The cost of using a block chain is what keeps the motives in line. Hosting costs money. And if hosting costs are not covered then it leaves the door open for loss of data or malicious motives. Tho I agree base chain transactions are often too expensive. This is solved by any one of the many scaling solutions that exists. Tho I admit they are all still pretty early tech. With such solutions costs should be at least 10x smaller.

I would argue the ability to have a single distributed ledger and its forever history, colloraboration tools and inability to have information left out is considerably more then a marginal improvement.