> This is the same argument for casinos but states don’t run those.

In most (or at least a lot of) countries states regulate casinos _so much_ than it becomes almost a technicality that casinos are privately owned.

Also with lotteries you have the scale factor -- in order to have an attractive lottery, you need a ton of ticket buyers, so if you have a national level lottery you can definitely make neighborhood lotteries way less appealing.

Blackjack and poker tables don't scale the same way.