

It’s not like they are a secret.
They’re also not public info, either. Typically they’re combined with name, address, etc for fraud protection, but those details are even easier to acquire than account numbers. The routing numbers are public information, though. In the result of a data breach, a bad actor has everything they need.
What are any potential hackers going to to with my bank account numbers?
Just about anything they want since they’ll likely have your personal details too. When adding a bank account to any of my utility payment accounts, there is no verification whatsoever; enter details, authorize payment.
I don’t use CashApp and the like, but in the past, PayPal would deposit a few cents into the account, and you had to verify ownership of the account by entering those random amounts into the signup form to complete the process. That’s also trivially defeated if enough of your data was breached and in the hands of an attacker (e.g. call the bank, pretend to be you, and ask for the info).
Not to mention, why would attackers in phishing/scam emails ask for bank details if they’re not secret or are useless?
Oh, we can do that too, at least to varying degrees. Depends on the bank and what services they offer.
My bank will at least do what’s called “Bill Pay”. It’s (mostly) the equivalent of me telling the bank to write and mail a check to a company on my behalf. I don’t currently have that setup, but it is something I’m looking into. It’s been available for a long time, but years and years ago when I looked into it, only certain companies/utilities were supported by my bank.