(depends on jurisdiction) there was already concept of pre-booked transport that was distinct from taxi and does not require taxi medaillon to operate. Uber just made pre-booked transport as convenient to use as taxi.
So it is not that Uber avoided taxi licencing 'because of app', but it avoided taxi licencing by providing slightly different service that do not fit into legal definition of regulated taxi services. And one could argue that these slight differences are in fact important, because the reason why taxis are tightly regulated are for reasons that mostly do not apply to Uber.
The Doctorow school argument, as best I can tell, would go 'the regulations on black car service were meant for things like limo services that don't compete directly with taxis, and once Uber started competing directly with taxis, regulators and authorities should have moved more aggressively to write new regulations/laws that regulated Uber the same way taxis are regulated.' They would not agree with "the reason why taxis are tightly regulated are for reasons that mostly do not apply to Uber."
And this is exactly why I think the question of "what is the correct way to regulate car ride services" shouldn't hinge on incumbency bias towards taxis, but actually ask the question of what is best for participants in the market (which doesn't just include taxis and Ubers but also includes public transportation and its users, for instance). But that doesn't fit neatly into Doctorow's enshitification narrative.
These claims of incumbency bias, based on a fragment of a sentence, seem unnecessarily presumptive.
I've read a bit of his work, seen a couple of his speeches, and don't have the same conclusions about his opinions. You could probably ask for clarification.