The only reason the city is doing this is because these ambulance contractors are sharks.
Ambulatory service is one of those things that should be ran by the city/state and not by some random private company. A private company in this case can only serve to make it much more expensive for the city and people needing emergency services while providing bad service and understaffing and underpaying their staff all at once. You'll get paramedics being paid $15/hr that charge $1500 for 10 minute ambulance ride where the contracting company pockets nearly everything.
I get it, cities don't like taxing people for ambulances, so that's why they try and contract it away to avoid that tax line item or savings needed to ultimately buy new medical equipment. That, however, kills people.
It's absurd that we can find it in our budgets to pay for fireman and police but for some reason anything related to medicine needs to be privately contracted out.