The over-supply of taxis has the opposite effect of a more regulated public transport. It does not reduce the total number of cars on the road. It's useful from a consumer standpoint but the low cost means people are less likely to use the state of the art elevated train and subway, both of which run under capacity.
"Price it like that and a lot less people would own cars." Possibly in other cities -- though I doubt it -- but it certainly didn't help in Bangkok. People don't buy cars because they need them, they buy cars because they want them. The number of news cars sold in the country per day is astounding (though the number escapes me) and that's despite the fact that they cost 50% - 350% more than the same cars in the US.
Bangkok needs to regulate the shit out of the taxi industry and make it more expensive to drive in the city if it wants to sort out its remaining traffic issues.
Uber can probably work in US cities that have the traffic capacity, but it's a horrible idea in congested areas.