They could, though then there would be more trust issues about who hosts and controls the database. A database of which every participant keeps a copy, and with strong guarantees about consistency between the copies, has pretty obvious attractions.

I am definitely not saying blockchain is the only or even the best way to achieve that! Just that this helps explain its appeal

Exactly. Big banks have already dealt with these trust issues through their teams of lawyers, longstanding partnerships, and reputation in the market.

I'm not saying big banks have nothing to gain, they do, but proportionally less than a smaller company that no one knows about. It allows "Bank of Mom & Pop USA" to confidentially do deals with "Little-Town Bank" Shanghai" without going through the mega-banks.