Those aren't direct comparisons. Hwy 407 is operated by its owners. I haven't been on it since my employer paid the tolls. I assume the Halifax bridges, like the Confederation bridge, are owned by the Crown (federal or provincial), but they are operated by a company under contract. I'm not enough of a traveller to comment on Canadian airports except that Pearson is chaos on a good day and T3 feels like you landed in Soviet Russia.
None of these are trying to provide a service on and alongside whoever owns the property. It would be like trying to operate a restaurant at Pearson, next door to one operated by the GTAA, and they get to say what hours you keep.
Other than a couple of FNs, what private rail carrier doesn't have freight revenue to backstop it (for than matter, what private carrier operates passenger service - don't say RMR?).
Absent significantly different legislation, I fail to see how a private carrier could do measurably better, particularly when they have to return a profit to their shareholders. No business exists to break even. If I recall, the corridor does 'turn a profit' but I assume that is operating costs only. Who do you think bought the fancy new trainsets?