I'm a bit horrified this is still a thing, too. Doing this just confirms you have the correct account and routing number, so you can deposit and withdrawal. It won't allow you to see transactions--will it?
FWIW, a minority of banks have "linked apps" that allow you to revoke access from the bank's website (some are clear they're restricting it to read-only access). But I'm not sure how consistent or widespread this kind of thing is. I doubt if you're offering a service like Plaid you could rely on only supporting these institutions.