Yeah, I do get your point, I think though that the value of currency is more to do with trusting the backers/issuers of the money, rather than any
direct relation to counterfeiting. If counterfeiting becomes too rife, then that will start to damage the trust of the money issuers. The relationship is complicated though.
The UK £1 counterfeit rate is almost unbelievably high, but the key point is that individuals aren't really affected by it. The coins are all 'good enough' that you are unlikely to ever have any rejected by a shop, so the end result is no-one cares about it. (Incidentally, it's actually harmful to check your own cash for counterfeits, since spending counterfeit money is a crime, but ignorance is an accepted defence.)
(I don't know where the buck stops. Do banks check for counterfeit coins and reject them from shop's cash deposits? I'm absolutely not trying to say that counterfeiting coins is a victimless crime, just wondering whether everyone shares the cost or whether it eventually catches up with one unlucky party)