Government provision of health insurance means that every procedure covered is a political issue (e.g. abortion for the left, sexual-orientation counselling for the right). This means that there will be nationwide winners and losers, and no-one but the rich will be able to simply change providers, as with a private market. As an example, look at how public schools are run: only the rich are able to opt out of government schooling.
American governments are not capable of running efficient programmes, because to a first approximation American government employment is a make-work program for people who can't get hired at anywhere that cares about competence. That means that a government insurance provider will be incompetent and inefficient.
To make things worse, the employees of said provider will be unionised, and that union will do its best to make it even more inefficient (e.g. take a look at the prison guards' unions).
I have pretty extensive experience with it at both local and state levels, with some experience on the Federal side. There are certain agencies and careers that seem to still attract decent folks, but they seem exceedingly rare.
If your only experience with government employees is asking them to provide service to you, then all you can comment on is how effective they were at doing that job. You cannot know what their general competence level is, nor can you know how they'd do outside of government employ, because you don't know what their job actually entails. I'll give you a hint, though - it's a lot more then helping you.
Even if you've worked for a government agency, which sounds unlikely based on your most recent post, you've only seen a tiny sliver of government employees. You can talk about the competence of that tiny sliver if you care to, but not all government employees.
Look, I get it, it's easy to complain about government workers. It's like complaining that all used car salesmen and mechanics are crooks. Using it in an attempt to prove a point though, is foolish, and that's exactly what you did.