Ah good point. Indeed much of what the government does could be accomplished by private groups.
So why should the government get involved? Let's look at the case of school meals. Many parents want them but it's not provided by the state school, so parents will team up to make it happen privately. This means negotiating with the school for access to a building on the premises, forming a committee to organize the whole thing (so having elections at periodic intervals to appoint the committee), hiring cooks, cleaners, security, etc., setting up a system for collecting money from parents, and finally establishing a process for decisions such as what to put on the menu.
We basically end up with a small task-specific government with its own laws (such as how decisions are made and how people are elected to the committee). So not only is it redundant with other local (e.g. city) governments, it also increases the complexity of everyone's life dramatically, as you have to deal with the public government plus all the private organizations, each with their own quirks.
This is why I view politics as a generic platform for debate on societal issues, and government as a framework for taking and implementing decisions. For this to be efficient it is important to have strong local governments at several levels (e.g. city, state, country) and choose wisely their respective prerogatives, such as city level for school meals, state level for school programs and country level for school certification. That does not mean there is no room for private initiatives, it just illustrates why government involvement could be a good option, sometimes.
As for the Constitution stuff, there's no question that a government should be monitored carefully and have limited powers (e.g. cannot force children to eat school meals), but this is different from saying it cannot offer school meals.