You're probably right, and I wouldn't be surprised at all if the government passed a law enforcing that some day.
But - in this particular case, I have to say that Uber had nothing on Yandex, who has been in the Russian maps and taxi business far longer and their navigation app is absolutely top notch (you should see how it lays out the route, and the funny jokes the navigation voice cracks when you're stuck in traffic), as well as their taxi app. Yandex is a very clever company and infrastructure questions aside, they are hard to compete with.
In fact, I'd argue that Yandex's technology is better in some respects than Uber or Apple's and Google's (if we're talking maps) but you will not see Yandex taxi service in the USA for the exact same reason you've stated, in the US it will be a US company.
BTW, Google is only #2 search engine in Russia as far as I know, simply because Yandex is better. I often find myself checking ya.ru when searching for Russian words when Google comes up empty.