An interesting thought. Governments have, over the years, privileged taxi providers in a number of ways. They've also imposed costs upon them: in the US things like taxi medallions (which can become very valuable in some cities) and in London by insisting on a couple of years as an apprentice doing things like The Knowledge and so on. Now governments are allowing companies like Uber (and Lyft, Sidecar and so on) to enter these markets without imposing the same costs upon those companies. This is akin to government taking the property of a citizen, similar to a compulsory purchase order to build a railway through the land. So, should governments be compensating those cab drivers? I think Mike Munger has the discussion and the conclusion correct here.
Yes, that cab license is property, akin to land. But compensation for the removal of a legal privilege it's doubtful should have been granted in the first place is not the same as compensation for the removal of a righteously owned piece of property.
The analogy I would use is that of free trade. It's often said that OK, perhaps a move to free trade is justified. But there's all sorts of people who gain from the current, not free, trade. So, those who will gain from the move should compensate those who lose. Which is an attractive idea: except, except. That except being, well, those who currently gain from not-free trade aren't currently sending cheques to those who suffer from not-free trade. So, why should the reciprocal be enforced?
We consumers are those who would have to compensate the cab drivers, through our taxes. The cab drivers aren't compensating us presently for the benefits to themselves of the restrictive legal privileges. So, the removal shouldn't lead to us having to compensate them.