So in practice it is very inconvenient not to have one and to be able to refuse anything you want or to have to accept anything. The workaround is to have a contractual clause that specifies exactly how a debt may be discharged.
In the case you mention this is called "defence of tender before claim". It means the person offered to the money but that was refused, so they go and pay it into court to protect themselves. In effect it means that if someone offers to settle in legal tender and is refused, then follow that legal procedure, then the creditor cannot do anything anymore expect recovering the money from the court.
Is that still the case?
Very German thing to do, yet in the UK I have not had a need to pay in cash, just use your card (or phone/watch if you are into that). Dunno if it was the money type, or just not want to be dealing with cash per se.