where's the data that those services actually didn't do their jobs in mixing their users' outputs? They probably did mix them, no?
Because if the entity you call "the wallet" actually mixes their users' outputs well, then who are you to tell everyone that "there's no underlying purpose for its existence"? If it's a service and does the service well, then it's up to you to use it, or not to use it.
The entity's wallet doesn't mix users' outputs at all.