The Liquid network comes to mind. Basically, any sort of system that allows users to swap coins and settle back to bitcoin is a layer 2 solution.
Banks could build an SQL database, generate a single Bitcoin address, and tell everyone to deposit there and prove they owned the originating address(es). You get credited in SQLcoins, which are centrally managed by a federation of banks. Once you want to go out, they send coins to an address of your choice.
If one of these layers becomes large enough, it might win the netwerk effect war and become the defacto layer 2 because everyone is on it.
That way I don't have to worry about integration between n layer 2s that my users are on (considering my users are unlikely to be on the same layer 2).