I am not disregarding your reason, it is valid. But me rejecting an unmixed coin is just as valid.
For your solution to work, it must be able to work in all scenarios. I just showed an scenario where it's invalid. That scenario is enough to prove the failure of coin filtering, because then all criminals will mix their coins and circumvent your system entirely. And surely they are already doing this.
Uhh no you would be completely wrong. I only need one scenario where it is useful. You have it backwards.