While I understand concerns about the lottery exploiting vulnerable people, one reason for having a state lottery is that it provides a legal alternative to illegal numbers rackets (https://en.wikipedia.org/wiki/Numbers_game), which were widespread before state lotteries became common. Criminal organizations profited from these underground games, often operating without oversight or consumer protections. A state-run lottery at least ensures transparency and directs revenue toward public services rather than illicit enterprises.
OTOH, legal lotteries get a lot more people to gamble. I suspect that people who gamble either way gamble more as well, though this needs a fact check that I don't know how to find.
Probably, although Australia's lottery operator experimented (briefly I understand) with making their lottery and wagering products available through a single website/gateway - I don't think it lasted because while there was some overlap between lottery players and gamblers, it wasn't big, and I think while gamblers could be enticed to buy lottery tickets, it was much harder to entice lottery players to dabble in betting on horses or sports games.
As a counterpoint, I know when Florida introduced their state lottery it really affected their other forms of legal gambling. This had the downside of killing off venues which employed many more people than a lottery ticket sold at a convenience store could ever sustain.
That's just a quality vs quality argument with an appeal to emotion at the end.
Not everyone impoverished by state sanctioned gambling would do so in an illegal only world. You can bicker about what the conversion ratio is but the fact of the matter is that it exists. And no, I don't know what it is.
If you really believe that argument, why don't we follow it to the logical conclusion, that all crimes should be made into state enterprises. State home burglary? State cryptocoin rugpull? State hitman? State jaywalking?
That's a slippery slope argument. Gambling fundamentally differs from crimes like burglary or fraud — gambling is a consensual activity that can be regulated and taxed, while burglary and fraud inherently harm unwilling victims.
State lotteries don't represent "state-run crime" but rather transform existing underground markets into legal, regulated alternatives. Illegal gambling operations have long existed, typically run by criminal organizations offering no consumer protections or public benefits. State lotteries provide transparency and channel revenue toward public services instead of organized crime.
Following your reasoning would suggest that legalizing and regulating alcohol or cannabis equates to "state burglary" or "state fraud" — clearly an absurd comparison. The objective isn't to convert crimes into government enterprises, but to acknowledge when prohibition is ineffective and provide a safer, regulated alternative.
As long as you do the math on the trade off of added safety vs added availability and pick the best option in every specific case you can apply the technique consistently to every situation without issue.