If all the people from the public don't care about your financial activity, it doesn't mean that a sub-group of people, which are specialized to analyzing financial activities, don't care either. They are caring more than anyone else.

It is evidently possible for the public to de-anonymize a large part of your Bitcoin financial activity. If you think that just by utilizing coin control you can protect yourself from firms which are funded by millions of dollars with the single scope of de-anonymizing as much blockchain activity as possible, then you're gravely mistaken. Even random people on this forum do it. You can't efficiently nor effectively gain privacy by coin control, you need at some point to enter a large pool of coins, which will make it hard for the observer to tell which is which afterwards (as in coinjoin).

So mixing is good, because it lets us define the limit of who's allowed to scrutinize our Bitcoin activity.