Regarding slings, though, is it true that in 5e they can still be used with shields given they require ammunition and therefore a spare hand to load? I don’t know enough about 5e but from reading the rules that’s what it looks like. If so, I guess slings are pretty niche and only really useful to druids who don’t have proficiency in any other ranged weapon unless their race gives them one.
Yes. most ranged weapons have either the two-handed or loading property, which means they need both hands for either wielding or re-loading, but slings are the exception, and they only need one hand, leaving your other hand free to have something else in it (my recommendation would be a shield, or use the Magic Stone cantrip).
As for the damages, if you look at the whole
weapon table spread out, you will notice that most of the damages are the same, meaning many of the weapons are mechanically the same, only differing in the type of damage they put out, and RP flavour. It's mostly for balance and keeping players on a more even field. Simple weapons do less damage and have less utility that martial weapons, reach weapons have their damage reduced because having a 10 foot attack reach is actually quite a good bonus, when it comes to mundane combat (remember that on tabletop, we often play on fixed grids or hexes, field control, terrain, and range are important).
My only big complaint is that a great axe should be 2d6, like the greatsword and maul, there's no reason for it not to be, and the only reason I can come up with as to why its a d12 is that it's the typical barbarian weapon, and barbarians are already using a d12, and the d12 is one of the lesser used dice.
