One difference between taxis and "everyone else" is that with everyone else, the business that does in their business is usually legal.
Uber and Lyft were largely operating illegally when they started in most cities. They ignored expensive licensing requirements. They ignored safety regulations. They ignored insurance requirements. They ignored price controls on fares. They ignored requirements to accommodate disabled people.
Taxi companies who were obeying all these rules (which all imposed costs on the taxi companies that Uber and Lyft did not have) had a reasonable expectation, perhaps even a right, to expect the city would force Uber and Lyft to follow those rules too, or would shut them down. But the cities didn't, so I think a good case can be made that the cities owe the taxi drivers a bailout.