Offering a choice between service provided by local government and a private business isn't really the kind of competition most people have in mind when they think of healthy markets.
Is the sort of choice that has been available in markets going back as long as governments and markets have existed though, so given there has never been a complete market that fulfils your definition of a healthy market, can we just look at whether there is some general economic benefit here rather than worrying about whether it is healthy, as if it is sick, it has managed fine so far for a good few thousand years, so it can't be too bad.
Is the sort of choice that has been available in markets going back as long as governments and markets have existed though, so given there has never been a complete market that fulfils your definition of a healthy market, can we just look at whether there is some general economic benefit here rather than worrying about whether it is healthy, as if it is sick, it has managed fine so far for a good few thousand years, so it can't be too bad.