Can a city or a municipal own and operate a tow service and have a profit? The city owns it's own tow trucks and rollbacks and offer what they call a city tow and it goes straight to their towlot.
I don't believe that it's expressly forbidden for a municipality to compete with the private sector, but it is certainly frowned upon by most.
Case in point, many cities are being ordered by state governments not to create their own citywide Wi-Fi networks because it competes with the private sector companies that provide this service.
City counsels have also "stepped-in" in these situations to protect private sector.
I really don't think it's that unusual for cities to engage in "for profit" activities.
Here if you want a culvert pipe installed in a ditch, you must pay the city to do it, and pay for the city to fill it with "their" dirt.
Now in your case, they are towing the vehicles to a city impound lot. Now if they start offering tows to a shop or to the owner's homes, then there's a real issue.
I deal with the same thing with lockouts, the bigger cities no longer do them but the smaller cities will still send out a cruiser to unlock a car. As far as I'm converned that's money straight out of the locksmiths' and towers' pockets.