This is exactly it. And it is not something that should be dismissed, it has pretty much been proven correct. In the US, before state run lotteries were present and popular, there were criminal run "numbers games" which were quite similar to lotteries but with much worse payout ratios and where the criminals that ran them often refused to pay for various reasons.
In the Scorcesse classic movie "Mean Streets" one of the storylines is about a kid that wins one of those numbers games but the person that runs the game refuses to pay him because he is of a mixed race.
Numbers games are very rare in the US nowadays and when present are only present in poor immigrant communities that do not know much about the state run lotteries. The state run lotteries did a pretty good job of getting rid of the numbers games and thus depriving organized crime of a source of revenue while providing better odds of success for lottery players and also taking in money for the government and thus saving taxpayer money.
The original lottery idea was also reasonably effective at keeping individual betting volumes low. They did this by making sure that each ticket was relatively cheap and required relatively large amount of work to determine the winner. Thus it was hard for someone to buy many tickets. Unfortunately, this is something that has slowly been eroding as lottery systems try to get more revenue and encourage compulsive buying.
So no I do not think state lotteries should be banned but it may be a good idea to change the rules for advertising or the games themselves to discourage individuals from blowing too much money on them.