Clearly, the fundamental argument here is about private provision of services vs. public provision of services. Is the optimal fire protection service one based on private subscriber payment to firefighters or a publicly (taxpayer or other government revenue-funded) operated fire department? The best IMO way to view this is to first clarify whether or not that service falls into the 'natural monopoly' category, at le…
Here's the problem with such schemes. Often both the providers and the customers of "augmenting services" will have an incentive to hollow out the state-provided service until it's substandard.
For instance, let's say the government provides "basic" health insurance but allows private plans. Then the providers of private plans will lobby the government to keep the "basic" service as low-quality as possible, so that people are incentivized to buy the private plans. Furthermore, those who purchase private plans will not personally benefit much from the state-provided scheme, so they will have little interest in its success and little desire to subsidize it.
In the worst case, the result is that the state-run service becomes permanently low-quality. Then people attribute this to public-sector inefficiency and say that "obviously" the free market would do a better job. Then the state-provided service gets abolished when it never had a chance to succeed.