Yes, but those leave more bread crumbs to catch the thieves. That's why the classic check fraud is to pay a mark with a fraudulent check for over the amount of the purchase and get them to send them the item and the overage. You have to physically (or use a legitimate account with an app to submit a photo of the check) present the check. That is more risk.
ACH is more of a b2b type relationship and your tracking bits to unwind the transaction. Once you set up an ACH, it is easy to access the vault as you have unlocked the door.
I'm not saying checks are totally foolproof. For example, If I owed a debt to a company and was in arrears, if I make arrangements to make a partial payment, I would NOT pay with a personal check. As you have pointed out, that gives them the routing and account numbers and they may raid the account for the full amount. Money orders only.
Like pad locks, it keeps honest people honest, but I still employ situational awareness.