The Swedish taxi market is not flooded, prices are not dumped, there aren't traffic jams. The major complaints are about tourists getting scammed by overpriced taxis (where the prices are legitimately posted in the window as super expensive) since they aren't prepared to have to compare pricing between taxis since everywhere else prices are regulated.
If that's the case, why aren't taxi businesses owned by the public? What makes taxi services different than water, sewer and municipal bus systems?
We have taxi services monopolizing entire markets just like ISPs (http://dailysignal.com/2016/10/19/taxi-monopolies-hurt-oppor...). These "Technically public but actually privately owned" business model appears to be the worst solution for any sort of consumer of these services.
For taxi private operators can make a business by offering additional services over the mandated taxi business (chauffeur services, longer term scheduled pickups, rides between municipalities, ...) The full picture is complex, though ...
The American experience I have had with taxis is that taxis are expensive, unreliable, and will try to ditch you if they deem your destination insufficiently lucrative. When you need them most, there's a very good chance that they won't show in a reasonable timeframe... or show at all. Which is to say that they avoid providing as many of the society-level benefits you describe as possible.
San Francisco in particular was a hell of useless taxis. For a long time, calling dispatch to get a taxi left you with odds of under 50% of one actually showing up.
Does this hold when the cost per mile/kilometer is still the same?