see
Pedantic Grognard
1) Wizards and sorcerers have proficiency with the sling because Gygax put it on the magic-users list.
2) Wizards and sorcerers are supposed to be worse at doing damage in physical combat than bards, clerics and rogues.
3) Uniform 5e proficiency bonuses to attack means the only way to express #2 is by making wizard weapons worse than the bard/cleric/rogue weapons.
Therefore, slings, which wizards can use, are worse than the short bow that they can't, but clerics and rogues can.
An alternative would be to remove slings from the sorcerer and wizard lists, make them a martial weapon better than the shortbow, and keep them under the longbow, so martial-types could choose either the cheap and inconspicuous sling (also useful if you are size S and can't use a heavy weapon without disadvanatge) or the more expensive and more conspicuous longbow.
2) Wizards and sorcerers are supposed to be worse at doing damage in physical combat than bards, clerics and rogues.
3) Uniform 5e proficiency bonuses to attack means the only way to express #2 is by making wizard weapons worse than the bard/cleric/rogue weapons.
Therefore, slings, which wizards can use, are worse than the short bow that they can't, but clerics and rogues can.
An alternative would be to remove slings from the sorcerer and wizard lists, make them a martial weapon better than the shortbow, and keep them under the longbow, so martial-types could choose either the cheap and inconspicuous sling (also useful if you are size S and can't use a heavy weapon without disadvanatge) or the more expensive and more conspicuous longbow.