> AFAIU, there are no nonfree payment services, except some crypto
  > payments.

In Europe, at least, there is bank transfer.  If you go to a bank
branch, I think, you can do transfers to someone else's account without
running any particular software.

Bank uses free software on their system?

Or are we to merely shift to services where nonfree software runs on somebody else's computer? 

Go to an internet kiosk and make the payment?

VR