> They have had fixed-price rides long before yandex did
As far as I remember RuTaxi had it even 4 years ago, but I not sure when they got mobile app since I only ever used website.
> AFAIU Uber has solved a problem nonexistent in many countries, and now tries to push its brand where there were better options long before Uber started in US.
As person who lived in both Russian and UK / London I understand why it's makes sense. Uber model works in countries that have one of the problems: bad public transportation (like in Russia) or very expensive taxi (like in London). Also they solve usual tourist problems that local services can't solve because you have to invest time to know what local service in $countryname is good or bad.
I have no idea about other countries, but service provided by same RuTaxi for instance was worse: old dirty cars, sometimes even drunk and just scary drivers. Thanks for competition all my rides become much more pleasant in last couple of years.
Also in Russia rides was more expensive: rides that cost $8 (~250RUB) back in 2012 now cost $3-4 (~150RUB). Recently I used Yandex taxi for ~5 minutes ride and paid $0.7 (30RUB).