A State coffee house - why not?

I have an idea: What would it be like if the state went into the competitive market? What would it be like, if the state, for example had a bank, an insurance company, hospitals, etc., yes and even a state coffee house.

If the state can make money from businesses, in competition with private sector, then why isn’t it doing it for the benefit of the public. I would like to choose if I shop with a private bank (and the one percent) or a state bank (with the public).

Then there would be a mixture of both capitalism and common ownership, where one could choose either or both, as they like.

I would like to point out that common ownership has been successful in many fields, for example in some countries hospitals are run by the state and that system is a lot cheaper than the private health care system of the United States. The major electrical companies in Iceland, which are profitable businesses, are owned by the state and communities and people are generally happy with that and need to pay less taxes. Back in the old days the Icelandic state ran the national post and telephone company and that used to be a great source of income, before the telephone part of it was privatized. In some countries, like in Sweden for example, a large part of the housing market is owned by the communities, I guess it is possible to offer lower rent by that arrangement, (there should be less demand for profit from the community itself than by private investors).

In some countries people are not free to run their own businesses, however with this system you are free to do so, but the state is also free to compete and possibly take a slice of the profit. This system could also possibly contribute to a fairer division of wealth.

I do not know how good this idea is, on the scale from bad to good, but I wanted to mention it which is now done.