There has to be a middle ground between the super-heavy regulation the taxi industry gets in most cities and the zero regulation that entities like Uber and such are currently subject to.
Bring in regulations that require:
All drivers driving for these companies must pass a background/driving history check (to make sure you dont have criminals driving for these companies or people with too many bad marks against their driving records).
All cars being used must pass a comprehensive safety inspection and roadworthy check before they can be used and then undergo annual inspections after that (to make sure the cars being used are safe and you dont have drivers driving with bald tyres or other faulty kits).
Companies must provide insurance coverage (with the minimum amounts set down in the regulations) for drivers (insurance that is active at all times when the driver is "on the clock" regardless of whether they are taking a passenger, heading to their next pickup or waiting around for a job)
Don't limit the number of cars or drivers.
Don't limit which vehicle models can be used for
Don't try and regulate the prices ride sharing entities can charge or the places they can operate to (including airports). Oh and don't require them to pay more money than anyone else either (e.g. requiring them to pay higher tolls than normal drivers or special surcharges at airports or other locations)
Don't require drivers to have expensive equipment (e.g. government-approved meters) in their cars.
Don't require drivers to have special paint schemes or logos or markings on their cars.
Don't require drivers to have special licenses.
With the companies dropping drivers who get bad reviews and the requirements for background checks to weed out the genuinely bad apples before things start, the risk of bad drivers is low (a driver who was driving erratically or speeding or driving whilst drunk would be quickly identified and given bad reviews/pushed out of the system. Same with a driver who e.g. threatened a passenger or tried to rob them)
If a passenger causes trouble (or worse tries to rob a driver or steal their car or beat them up) the driver can give the passenger a negative review or for more serious cases, report the passenger to the cops (who can find out the passengers details since all passengers are tracked through the ride-share systems)