Are taxi cars safer than personal cars?

No.

There was a time (and in Great Britain this is still partially true) when taxi drivers were well trained professsionals.

Those days are gone. Now it is a long-hour, low-pay job mostly for immigrants in the US. Very little training and crappy vehicles.

Taxis or Ubers are no safer than private autos.

In BC you have to have a class 4 to drive a taxi, and that is a bit more than a regular class 5 that you need for cars and pick up trucks.
Also a taxi is deemed a commercial vehicle and is subject to safety inspections for such.

Professional doesn’t always = safe.

No, not just because they are taxis. It is my hope that safety is a concern for the purchaser when purchasing automobiles to be used to transport the public.

In lots of places, taxis are former police cars. The car itself depends on the state, city, company and owner.

The training is non existent. Hiring does include a printout of the applicant’s driving record.

In some places, the cab is owned by the company, and leased out to drivers. In other places, the cab is independently owned, and either driven by the owner, or leased out.
I once worked with an owner who drove a shift, and leased it to me during his down time.

Fares we’re especially safe with me.
I drove nights. Managers at strip clubs knew they could count on me to drive girls home safely and discreetly. The dispatcher counted on me to convey kids whenever any had to be transported during seedy hours. I was used occasionally to transport women escaping brutal men. Once, I picked up a fellow who’d just been threatened at gunpoint.
Always, I considered myself responsible for the safety of anyone who was in my cab. Lots of drivers do feel like that, but lots don’t. For instance, I once carried an unconscious fare who was drunk to the door of the address he’d given me. I rang the bell. His mother answered. She was quite surprised. She told me normally he would be left in the front yard with an empty wallet.