There is no "natural mixing" that occurs, really. Inputs to a transaction are all controlled by the same party, unless you are using a mixing protocol like coinjoin.
Let's imagine a bitcoin thief sends three "black" outputs to three recipients whom were not involved with the original crime. The first recipient then uses this black output along with two other white outputs to purchase something from Overstock. The output that Overstock receives can now be thought of as gray and is an example of "natural mixing."
It is the Overstock customer who screwed up here, and and Overstock may well reject the purchase, or require additional documentation and reporting. Let's say Overstock rejects the purchase and sends the coins back. The customer now has mixed gray coins that may be difficult to use for anything, instead of white coins that were clearly usable.
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I think I see what you're saying Smooth, but I think you're missing the point I'm trying to make: the black listing can occur
after the transactions took place. So suddenly Overstock is stuck with coins that it accepted according to the rules (they appeared to be "white"), but that are now suddenly gray or black. And if this can happen, then either the currency system is essentially unusable or the blacklisting efforts are largely ignored.
Again, or they just act conservatively and try to avoid accepting coins that place them at this risk, which means rejecting coins of unclear or uncertain origin. If your coins come from some part of the explicitly-legal the walled garden (Coinbase, Bitpay, etc.), they will welcome you with open arms. Otherwise they may take a pass, even if you coins are (or might be) perfectly fine.
I don't disagree the currency system may become unusable under these conditions, or have limited potential. Fungibility is very important. It just isn't assured by the technology in any way I see.
you're missing the point that it might not need to be assured by the technology.
what might assure fungibility is mere market behavior. it's quite possible the community herd understands that by accepting blacklisted coins we encourage a massive crowd effect which might positively determine Bitcoin's outcome as a successful currency despite your individual technical privacy concerns.