1. That public internet would suck because all public projects suck (and cite examples).
2. That private companies wouldn't be able to compete with public ones.
They cannot both be true. If the public offering was as bad as you claim, private companies could compete (e.g. on quality).
So which is it? Either public companies suck and therefore private companies would be able to compete (by virtue of them sucking less presumably) OR public companies don't suck and the private companies wouldn't be able to compete.
Your whole post reads like one of those propaganda pieces put out by the far right, interest groups, or think tanks. Just generic "all public services are terrible" then switch it up into "it is unfair that companies have to compete with taxes!"
One could take the logic in your post and use it to literally argue that all public entities ever should be closed and privatised. Even things like cops, fire services, and so on could be hit by that logic. There's no limits.
The current telecom oligopoly is bad, but a government-run monopoly is the one thing that could be worse. Now, public money going to build last-mile fiber which is then leased to competing ISPs to create a functioning marketplace (neither corporate oligopoly nor government monopoly, but a true economics-textbook 'free market') sounds like something that could be a good use of public money & power.
Unless those private companies are legally prohibited from competing, or are prohibited from practically competing by things like red tape or fees for constructing infrastructure.