Having a single state-sanctioned business (and therefore backed by the threat of violence) is somehow less monopolistic than having a free market where the best service provider is rewarded by becoming the most popular and profitable one?
There's one Uber and maybe Lyft if you're lucky. In the grey-area taxi market, they might fit the definition of a monopoly. I wouldn't argue that though because I know nothing about that market and reading that sentence back makes me laugh.
Microsoft operated in a relatively free market and was the arguably the best software provider as they were the most popular and profitable one for quite some time. They were also deemed a monopoly.