Speaking as someone who who lived in Houston for the last two years, I disagree about Houstonians not wanting Uber/taxis. Yes, we all have cars, but I can't tell you how many times I would have preferred not to drive on Friday/Saturday nights (as a 20/almost 30-something). We wind up driving because, as you say, taxis were rare, and when they were around they were all pretty awful. Not living there now, but I'm very much looking forward to visiting Uber/Lyft.
Also, as an aside, I knew someone in Houston who was in city government, and it's amazing how some of these dynamics work. Basically, this change was blocked by the yellow cab lobby for the last two years, and only for the price of about $5,000 of campaign contributions per city council seat. Local politics are insane.