The Satoshi quote of "no free lunch" is kind of erroneous as both fiat and Bitcoin require overhead just to exist at all while gold and silver do not. This is probably the biggest Satoshi red herring that exists. Nobody is forcing you to pay to store it in someone else's vault. You cannot use the word "ideal money" to describe something that requires overhead just to exist when there are alternatives that don't
You obviously forget about trivial wear and tear that gold and silver coins are susceptible to. It is also a kind of overhead, and given the level of circulation these coins will be exposed to, it will be insurmountable. And I'm not even talking about deliberate debasement of coins either by governments or ordinary people who would try to chip a bit of metal from these coins every other day. And then you would hit directly into the modern variety of Gresham's law because prices of these precious metals change differently and the nominal value of coins will quickly cease to match the value of metal in them with all ensuing consequences...
In short, your idea of using such coins today seems to be pretty much stillborn
Paper is always going to be Keynesian by definition, and even if you could somehow overcome that logic and eliminate the horde of parasitic technocrats, you'd still have to constantly reprint the bills, and using metal coins would eventually just be sending you back to gold and silver anyway
Overhead in using gold or silver coins will be devastating up to a point where they are not usable altogether (see above)