You just listed why Uber is so valuable: none of the others have anywhere near the global range Uber has. Even if Uber banned in a couple European countries they're still widespread enough worldwide to be a better alternative than <no similarly-sized competition to insert here> because of a simple fact: I already have the app setup and running on my phone, which isn't true for any other ones you listed, which either don't operate in the continent at all or are regional to the point of near-uselessness.

In other words: when I travel somewhere, be that a different city or country, I'll by default have Uber already running on my phone; I don't have whatever regional equivalent there is there. This also works the other way around: because I have Uber setup for whenever I travel, I end up using it over any local apps because it's already there and another taxi app offers me nothing that Uber doesn't. I'd love for Lyft or anything similar to get off their asses and expand internationally but I suspect I'll be an old man by the time that happens in any serious capacity.

edit: for example you said you work for Grab. Ok, granted that people from other countries are likely just a tiny market not worth chasing so you don't particularly care whether I use Uber whenever I visit SG, that's fine. But users in SG surely care about only needing one application whenever they travel abroad, which drives adoption towards Uber in Grab's detriment; that's a big reason why Uber is so valuable. From reading the Grab website it looks like that's exactly what Grab is chasing too: expansion into other markets (and props for already supporting multiple countries, along with the app being totally fine with my unsupported country phone number).

Problem is only Lyft is somewhat big. When you say "There's a dozen copycats that do it exactly as well as Uber", that includes operating in several markets too, no?