This isn't about protecting the taxi industry- as you rightly point out, many taxi drivers are also contractors. Instead, this is about properly pricing labor. The gig economy works now because companies like Uber (and many others) externalize the real cost of hiring labor.

It doesn't make sense to pay people low wages to the point where they need governmental assistance in the form of food stamps and BMR housing, and then pass on the savings to private companies who do their best to avoid paying the taxes that fund those programs. It ends up being other, traditionally employed FTEs who subsidize this business model via their own tax bills.