As to firefighters, here (and in most other cities, I think) they earn their living as EMT's. The fire coverage is something cities must provide, but actual fires are fairly rare. Firemen are assigned collateral duties to fill their time.
Most of these companies could effectively run fire services as well. Some municipalities already contract them out.
The average Paramedic on a Fire department in a large city makes $60, 000 or more a year + overtime and only works 7 24 hr shifts a month. A private Paramedic makes around $35,000 and works 16-10 or 13-12 hour shifts a month. That savings doesn't even bring up the lower costs of health care and retirement.