This is how Venmo does it so they don't have to make you do the "verify two microdeposits" process, and it's getting more popular. I think because when you give your login you're giving over complete access so bank is not liable for fraud.
I had to do it when I signed up. That's why the history of my interaction with Venmo was (1) change bank password, (2) accept the money from the person who would only pay using Venmo, (3) change bank password back so that Venmo / late hackers into Venmo databases don't get any ideas.