My second paragraph spoke to this point. If coins mixed with black coins become black, then every coin is at risk of turning black after it's already been accepted for payment. So I don't think the currency system works at all at that point.
We'll see. Maybe it doesn't work at all, or at least ends up being somewhat similar to traditional banking where there are extensive KYC/AML requirements. You realize if Bitcoin has any chance of becoming globally dominant with trillions in market cap than the market is pricing that probability at roughly 0.1% (or possibly much less if there are non-dominant, non-zero outcomes), right?
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.
By contrast if the customer had kept the black coins segregated and rejected them (sent them back and demanded "real" coins instead), this problem wouldn't occur. This in turn will cause this customer to be a lot more careful who he receives coins from and under what conditions and they get mixed together. Which is precisely not the definition of fungibility.
You are assuming, I think, that coin control doesn't exist or isn't used. But people will use it if they have an incentive to do so. If I receive my salary via a clearly-legal regulated (whitelisted) process I probably won't want to taint those coins and create unnecessary problems for myself by mixing them with coins I received somewhere more questionable. If I accept questionable coins at all, I'll keep them separate. It then becomes unclear whether anyone will accept these lemons.
BTW, it doesn't really make sense for a freshly minted coin to have a shade of gray. Not sure what you are talking about there. Coins are either born clearly white/legal (mined via a legal, possibly-regulated process) or born black (mined otherwise).
It depends how you define taint. Imagine that a miner mines a block that awarded him 1 BTC in transaction fees. Later it's learned that those transaction fees were from coins involved in a crime (and retroactively blacklisted). Is the 26 BTC coinbase reward now "white," "black," or "gray?
If the answer is "white," then this is a great loophole for whitening coins. If the answer is "black" then this currency system is probably useless.
There is not really a "loophole" because we were discussing in explicitly-legal, possibly regulated mining process which would certainly in-effect (or actual practice) whitelist the coins. That would not include deliberate money laundering.