You obviously forget about trivial wear and tear that gold and silver coins are susceptible to.
This is mostly just an appearance thing unless people are clipping the coins, in which case vendors would probably either reject them or turn you in to local lawmen who had punishments for doing things like this like death (lol). The US government also used to offer a service to turn your bullion into govt coins for free I think. It's overall not a big deal since the things are still recognizable a thousand years later. They don't actually require overhead to "exist".
Why use gold and silver coins if we could just go back to gold exchange standard under which paper money was freely exchanged to gold at a fixed rate? I guess I know what you are going to reply, namely, that governments would inevitably end up printing more paper money than they have gold in their vaults. Very much like they diminished the content of precious metal in the coins they also happened to mint...
See the history of Roman Empire and their gold coins that ended up without any gold in them