I don't see that the OP has mixed up anything at all.
The question is what benefits would accrue from a privatization of an ATC system that handles far more traffic terminating and originating at far busier airports than Canada and all of the other countries with privatized ATC have combined.
We do have a terminal problem in some US markets, but that's a matter of too many flights trying to use too little pavement. This works pretty well until weather intervenes and no amount of ATC improvement can help with that.
In short, ATC privatization seems like a solution in search of a problem, or maybe someone's wet dream about the profits to be reaped, if only in outsized management salaries in some non-profit scheme.
Thanks, but no.