The way I see it, this is not true. No amount of extra work will enable researches (or whoever) to prove address X is now the owner of the "red flag coins". Any of the output addresses of the coinjoin tx could be the "real" owner.
Please explain if I'm wrong.
You're right, this removes proof that the funds were yours. You have plausible deniability. They only could be yours, as your address is one of those publicly associated with the red flag coins. As you can tell this is somewhat different to the functionality of a tumbler, where at the end of the day your new address is not associated with the red flag coins on the public record.
I understand you reasoning, but I'm not sure this distinction can be made:
If you argue using coin taint, consider that you might also end up with other tainted coins -- let's say some purple coins -- coming from your traditional tumbler. The tumbler doesn't magically give you "clean" coins either (unless it distributed freshly mined ones somehow, and here you can see the upside of buying mining contracts and such, but that's not tumbling, but selling clean coins), but give you coins from other users, likely to have some bad taste to them, too.
So tumbling the coins equally leaves you with nothing more than plausible deniability and a bunch of tainted coins. You might have successfully removed your red taint, but are now stuck with purple taint.
I don't quite see a qualitative difference here.
Maybe we'd have to define more exactly the goal(s) we want to achieve here?
If we want to make bitcoin more anonymous in general, for example, widespread frequent casual use of coinjoin seems to be a very good way.
If we want to specifically and completely remove a certain colored taint from some coins, the use of a traditional "laundry" may be more adequate.