The taxi analogy isn't the same. The rates are being set by the local government, not some non-government third-party whom they work with like perhaps the people who actually own the medallions (most are loaned out) or the people who lease out usage of the vehicles, etc. If those places were setting rates on what could be charged then I'd say there's an argument to be made. Also, let's not forget why the government put in those rules on setting the rates in the first place - consumer protection. Cabbies were routinely ripping people off.

Furthermore, it's not just one thing. It's a set of criteria/tests that for certain states like CA and NJ are defined in the law. Taken in aggregate and not just on one single characteristic of the employment a determination can be made.

In NYC and possibly other municipalities, the government sets the minimum rate for uber/lyft. Are they more or less of a contractor then?

This isn't wholesale true. Some areas are highly regulated (see Tokyo) and some are not regulated at all. Also, local government sets a MAXIMUM rate in some jurisdictions. The taxis then choose to set the rate the driver can get paid.

If Uber drivers are taxi drivers, which Uber claims they aren't (they're limousine drivers legally), then they are running illegal taxi services. It seems mighty convenient to pick and choose from laws only when it suits Uber's bottom line.