Since decent online banks will let you save the details of recipients, in practice it is very smooth and uncomplicated.
You could also receive and send invoices by fax, and there's nothing wrong with that.
Sure, it works. But it's super slow and archaic. In the same way some people think people writing personal checks works, but others think its ridiculous.
There's nothing slow or archaic about that, at least I haven't noticed that after a few thousand invoices sent and received by e-mail. With modern banks you can even make batch payment of invoices by uploading a csv file.