I'm afraid you're wrong here. Don't compare cash with Bitcoin. Restaurants, barber shops, grocery stores, hotels, markets, and almost all business establishments don't have mechanisms in tracking whether your money is dirty or not. That's different with a lot of duly licensed or registered crypto companies. Centralized and regulated crypto platforms such as exchanges, payment processors, lending, crypto banks, and so on are normally AML-compliant, which means they have AML bots and tracking software running 24/7 to guard against dirty coins.
The moment your coins are marked dirty, you'll be in trouble. Your coin might be rejected. You might not be allowed to do trading or conversion. You might get banned. Your account could be locked or your funds frozen or even confiscated. Your wallet could be blacklisted. You could be fined. You could even be prosecuted.
There ain't no difference between so-called "dirty" coins and normal coins.
It can be argued, that every single coin is going to be tainted by the year 2147 - when the last block reward is mined. Think about that for a second.
Every coin you touch will either have traces of mixers, coinjoins, casinos or ponzi schemes (because scammers dump their coins on exchanges).
So, it is suicide to even worry about the issue of tainting in the first place. In chess we call this "zugzwang" - It's your turn to move, but all your moves are bad.
But since you are not obliged to move your coins, then by all means don't, unless you're trying to pay someone/thing.