If they actually operated in a disinterested way, sure, but how many different forms of advertising do you see the lotto being promoted in? Doesn't seem disinterested to me.

What? States make buckets of money from gambling. They typically claimed it was "for education" but money is fungible and our other taxes never went down, so anything it offsets in one budget just leaves more money for other budgets.

The real reason they can do it is they (the state) have a monopoly on violence and you don't.

Or that they have a monopoly on lawmaking.

Nobody is going to start a violent revolution over lottery tickets.

Read my second sentence again.

I read your second sentence but I don't get it. Isn't generating profit for the state literally the entire point of the lottery? Who is arguing that it doesn't do that in theory or practice?

Profit motive implies profit maximization behavior or mandates. A state-run lottery should not have that. Again, in theory.