€0.01 coins have a volume of ~0.346ml, gold has a density of 19.3g/ml and a current price of 60.89 USD/g, so a eurocent-sized gold coin would be worth 407.02 USD :)
Yeah, but you're still having to pass through Coinbase or any other exchange, and they can remove it from you there. That's the point, if Bitcoin needs an exchange to be functional you're losing all the differential features that Bitcoin has.
Gold is less volatile, and the value of the volume of a €2 coin in gold is 9 months of El Salvador nominal GDP per capita.
Or the gold could be stored elsewhere and accessed via an app, with exactly the sort of database every bank already uses.
Either way, BTC adds nothing. Apps might, depending on the banking infrastructure, but BTC itself? Nada.