Not saying it's the best situation but if the choice is between the mob running it, capitalist corporations running it, and the state running it, I'd pick the state.
The state has an incentive to decrease problem gambling. Even if you ignore any democratic pressures from the people who don't like gambling being pushed, the state also has to bear the cost of addicts with social services so it's monetarily incentivized to reduce problem gambling.
Yeah but that incentive exists for any organization running gambling. It's just that the mob/companies will pursue that motive more ruthlessly because:
The state is more accountable to the public and public opinion than a company. A company is only accountable to its shareholders who will almost always tell it to pursue profits at all costs. The state, at least in a democratic system, is accountable to the people. People can vote out a city council pushing gambling to increase revenue, they can't vote out the board of draft kings.
The state bears some of the cost of addiction so they have some incentive to not let it get out of hand. A destitute gambler is more likely to use social services, to commit crime, abuse their family etc. which the state has to pay for in some way. Also there's lost sales tax revenue if they can't buy anything else and they're more likely to stop paying property tax or get their home foreclosed, sold for a lower price lowering the assessed value and the property tax you can charge. All of these costs are completely externalized for companies / the mob so they can, and usually do, ignore them.
Also the money can go to actually good causes as opposed to the pocket of the draft king's CEO or the mob boss. You can even theoretically set a cap for revenue, say the state can only make $10 million off of gambling, and the rest is proportionally refunded to the gamblers, you'd never see that in a for-profit enterprise like a company or the mob.