One of the key features of these apps is that you only need the phone in order to make transfers, that allows you to avoid asking for the account number to anyone.
For anyone in the US, if I have your bank account number, I can steal your money. I strongly advise you not to share your account number with me or anyone else. I have to commit fraud in order to steal your money, making it a crime, but stealing's a crime in the first place, so that's not going to deter thieves.
My understanding is that this is no longer true: only a relatively small set of trusted entities can perform a direct debit (check or check substitute not present) from an account number without having to perform additional verification. The ones that I’ve personally seen are utilities and colleges; I tried to do the same with a friend once (so he could pay me back for something without having any fees) and our banks refused the transaction because our account names did not match.
Jeremy Clarkson fell victim to this. He published his bank details in his column to prove it was no big deal, and someone set up a £500 direct debit to charity.
Replying to myself here since the edit time expired: this does of course depend on where you live; in the context of the thread and the while fintech popularity in various places around the world and the EU not really having much use for that, this is because you can safely transfer money around without the risk of someone abusing your 'secret bank number'.
In the US and probably other places as well this is more like an SSN where just having the number allows you to do all sorts of (criminal) abusive things.