Should? Probably. It makes money for the state. Other states nearby in the Deep South (Georgia for example) has had lotteries for 20+ years.
A lottery is one of those opt-in things – people are not forced to play; it’s a personal choice on whether to buy a ticket or not.
But Alabama is the old religious South at it worst, and the Baptists probably think that the state has no place offering gambling, because it’s evil – even though gambling is in the bible.
The end result is that if people can’t buy lottery tickets in Alabama, they drive to Florida or Georgia or Tennessee or even Mississippi.