Exchanges could act as channel factories, for example, today they batch a bunch of withdrawals into a single transaction, there's really no reason why they couldn't simply open a channel for each person in that.

It can be a third-party or you could also run one yourself, there's nothing stopping you.

I wouldn't be surprised to see counterparts, just like email is "mail on the internet", but there are also fairly novel concepts like flash loans which are just not possible in current financial system.