Are you American?
No.
If the government service is crap, replace the government, or employ better people.
Absolutely. Sadly it's hard to fire civil servants so that they can be replaced by better ones, witness the UKs Home Office, HMRC, DWP, etc.
Moving to the private sector is NEVER the solution, it adds to costs with shareholder dividends and profits etc.
Ah, someone who's been drinking the kool-aid, and has apparently never actually lived for any amount of time in a place where such services are state-run.
There's a wide assumption that government-run services don't need to make a profit, and so can be run economically for the benefit of the users. That's complete bullshit.
Even governments have to invest in services, and do do so they either need tax money, or they take out loans whose interest is paid from tax money. They could, of course, make a profit and even pay taxes, but under your plans that isn't allowed, so the taxpayer has to fork out instead. Lose-lose. Without enough investment, of course, the services themselves are crap. Think 1970's GPO phone service and BA internal UK flight prices (£250 return Belfast-London, that's £1000 in today's money, whereas EasyJet & co charge 1/10th of that).
Furthermore, because the civil servants who run the state departments who run those services think they don't have to make a profit they develop a "there's always more money" mindset, so everything is run inefficiently. They don't need to care about improving "service" because they get paid anyway, so running a minimum service is all they need to do. There's no benefit in improving service, because they don't get more pay or more money for doing so.
The right wing have convinced you that government run services are crap
No, 40-odd years of living in countries, both left- and right-wing, where the services are government-run have convinced me they're crap.
Leave cars and TVs etc. to the private sector, but social resources that are monopolies should always be Nationalised.
There a a few state-mandated services, like Police and prisons, which clearly need to be state run. Nothing else should be, it is always an economic and social disaster.