While I agree with your general sentiment, you are missing two key points:
1. While "me driving to work" and "me driving someone else to work for compensation" are the same physical actions, they have very different intents and motives, so they are NOT the same. As another posted wrote (and I have friends who confirm) - as a private pilot you CANNOT take passengers on flights for compensation, even if you are flying the same aircraft you normally fly alone (or with non-paying passengers).
2. The risks to a passenger vs another driver are very different. If I'm a passenger in an ill-maintained vehicle, I have no control over my situation. If the axle breaks then I have to suffer whatever consequences happen. But if I'm a different driver on the road - I have options in terms of what I can do with my vehicle, when the other vehicle's axle breaks - I can slam on the brakes, swerve around, etc. As a driver, I might be able to avoid the dangerous situation, or I might make the dangerous situations worse -- but being in control of a vehicle I have options that the passenger does not.
So yes, I think it is legitimate for cab / taxi services to be held to a higher standard than regular drivers.
That said, I agree we have too many terrible drivers on American roads (I'm assuming you are American), and I would not be opposed to elevating the standards for everyone! But that is orthogonal to if cabs / taxis should be held to a higher standard than regular drivers - I would support both.