Regardless of who that person is, the organization they lead would be absolutely massive, with tens of thousands of employees, a 10 figure (possibly 11 figure if all transportation is thrown in) operating budget, and another 10 figure capital budget. And leading something that big would inevitably give them substantial profile and clout. It would be the one agency that literally impact every GTA resident daily, from the minute they leave home.
The other problem is that it really becomes hard to suggest that an agency that could be a third to half the size of our defence department, not have a democratically accountable head at the top. They'd need the sort of standard government (political) Minister and (bureaucrat) Deputy Minister setup to run something like this, at minimum. Ultimately, if you're telling mayors and city councils what to do, that can't come from an unelected bureaucrat.
All that said, I would love to see Metrolinx become the GTA's version of TfL.