Many upstanding people—and even large companies like payment processors!—process their received funds through a mixer “just to be safe”, i.e. to escape any coincidental untoward paper-trail that attaches to their funds two or three steps back.

You know how they say that every US dollar bill has a little cocaine on it? Using your suggestion, every dollar bill would be marked tainted as drug proceeds.

That's as dumb as laundering clean money “just to be safe” or covering up a crime you didn't commit “just to be safe” (hey Reiser). If your coins are clean, mixers make them dirtier and this has been known all along.

If you're e.g. a retailer, you can maybe know your coins are clean one step out, but you can't know if they're clean for their whole traceable history without standing up a fancy Network Analysis OLAP cluster and hitting it with some really high-cost queries.

Let me put it this way: what would you do with your float if you run a convenience store in a bad part of town, and know that there are marked bills floating around in the local economy, and that the police might pop in at random one day and take them out of your till? Well, you'd probably deposit your float in your local bank at the end of each day, and then get new, guaranteed-unmarked bills from the bank. That's mixing! It's not money laundering, just mixing. You're removing the potential liability of being blamed for what your customers' employers' customers' employers did.

They're not trying to hide the proceeds of a crime, they just want to protect their privacy from anyone snooping on the transactions. The government is not the only party interested in how people are spending their money, and criminals are not the only ones with a legitimate reason to want to keep their financial dealings private.

This may result in tainting large part of bitcoin in circulation.

If someone buys a coffee with tainted coins, is the cafeteria now responsible for querying the registry to reject the transaction? Or it risks to have whole daily turnover, if spent together, end up tainted?

I'not saying that it's going to happen, but it certainly seems plausible to have laws that merchants who violate some blacklist forfeit their daily turnover, there are existing laws with much, much harsher consequences.