As a general matter, I think the best reason for government not to go around competing with private industry isn't that doing so inherently diminishes our freedom, but because it's just not worth the effort, and much of the time it isn't going to provide any benefit to consumers. It wouldn't be tyrannical for the federal government to produce its own brand of cola, but it would be pointless, since they're unlikely to make something people will like better than Coke or Pepsi, and consumers seem to be perfectly happy with their current cola options. On the other hand, there are some areas where the market has clearly failed—health insurance for senior citizens, for instance (and, I'd argue, everyone else too, but that's a separate topic)—where it makes sense for the government to step in.
But what about areas where the market in question involves private companies helping consumers interact with the government itself? And where there isn't a particularly egregious market failure, but the government could clearly offer people the same service for which they're now paying, but at a lower price? Like, say, zero? In that case, it would be hard to argue that the government would be outside its rights if it made it easier for people to interact with it, solely on the basis that those private companies might suffer from the competition. Well, according to a story from Pro Publica, that's what's happening in the area of tax preparation: