In most of mainland Europe everyone pays everyone through online banking. In Denmark people put their account details on their web sites and letterheads.
There is really reason why you couldn't do the same here even with first time vendors. Except that some banks make it really hard to do.
My old bank Wellsfargo had me sign up for something called I think DirectPay where you could do it easily. But my new bank CitiBank make it just as easy as in Europe from both my personal and business accounts to send money.
This love afair of checks that American business has is all about float and frankly I am incredibly annoyed that all my clients insist on paying me by check.