Sure, but what Uber offers is to make this ubiquitous and save me from having to learn the subtle variations of the local taxi markets in each place I visit.
Your argument boils down to: they are not taxi service, because they are ubiquitous.
There is nothing about taxi definition that would exclude ubiquitous from it. There is nothing about taxi definition that would exclude companies with easy to use apps from it etc.
I'm not arguing that they're not a taxi service.
Colloquially they definitely are, and I don't know enough about the legal definitions to have an option on that aspect. I was just pointing out their competitive advantage over local taxi companies with local apps.
If there are differences it'd be (partly) b/c of regulation which the topic is all about. By all means if Uber feel like using licensed drivers, cars etc. as they apply to a specific country, they can keep their ubiquitous app.
For instance: enough cities may not have preferred/dedicated public transport lane which makes significant costs based on waiting times, rather than distance: hence pre-agreed price is an estimate at best.
To me: Uber is a taxi company through and through and if there are local regulation Uber should not be able to circumvent them.
