Thanks for the feedback! I’m aware that checks (and “instant” payments like PayPal, Venmo, Zelle) are settled via ACH; as other commenters have pointed out for me, the claim was that individuals can’t make “raw” ACH transactions.

As for sending money via routing and account number: I’ve received conflicting information from different banks on how acceptable this is. The university I went to allowed it as a way to pay tuition (you could give them your account number and they would debit you), but every bank that I’ve privately banked with has told me that I need to own or be responsible for both accounts in order to do a “direct” (i.e. non-cheque) transfer. But I don’t know whether that’s just a policy thing among financial institutions.