That can be true in some cases, for sure. For example we probably don't want government-run fast food or government-run rental cars because of that "race to the bottom" you're citing. But there are also things where that 20% margin actually makes it more expensive. Managing utility poles and electrical infrastructure is a pretty good example. There's a strong public interest in having poles and electrical wiring in every house, and so a government monopoly is probably good. You're not going to have more than one electrical system in an area, and if you did it would substantially increase cost of delivery. Roads are another good example -- you're not going to find yourself in possession of more than one driveway to your house and pay differing prices for different driveways. You could also argue that things like healthcare, education, and maintenance of shared public spaces is also something we should probably do through government because consolidated physical infrastructure allows us to substantially reduce the cost to the taxpayer versus what they will pay out of pocket when these things are privatized, and you can experience those costs when you use for-profit public spaces like indoor play parks and such. And then the elimination of that profit motive absolutely does reduce costs even further. There are examples of this you can look at where IE emergency services are privatized and they immediately get more expensive for everyone and with less actual service provided.
I think it will greatly benefit politics in the US to stop looking at this tension between government services and private services as all or nothing and start thinking about what is most beneficial to the public economically.