I think where it breaks down is that even 1 coin a day is already insanely high for medieval times. A modest person would earn maybe 10 coins a year, if they are somewhat qualified or really good at what they do. And that’s only for people living in cities.
For most people, living in the countryside, they would see very little currency. You’d mostly own what you could build, grow, raise or barter, and you’d rarely have enough surplus that you could sell for coin. To get 1 gold coin you’d have to sell 2 or 3 sheep but how often would a modest person have animals they don’t absolutely need to keep ? Not something that’s going to happen every year.
Even the innkeeper would not see 365 gold coins a year, that kind of revenue would be way upper class.
If i recall correctly, you can hammer the coin when it’s cold to put the decorations on it, but you still need to melt the metal at some point to get it at the right thickness and give it the circular shape. I may be wrong tho