If we assume the government health service is behaving in its own self interest,

Given they way other government services tend to behave this is highly dubious.

The most obvious examples would be schemes to get people to stop smoking or lose weight, that the government provides freely because they are less expensive than the projected cost of the illnesses that would arise without such intervention.

The problem is that the way these kinds of schemes tend to work in practice has a lot more to do with whatever the currently fashionable moral panic is than any rational analysis.