Thinking about it, we can reference regional mythology.
Just wanted to say that this post is very well though out, and it's going to be my headcanon for anything HP related going forward. It's awesome.
It probably is superior is some aspects (with the clear disadvantage that those taught by it can't really use magic if it is taken away), otherwise why use and make it, in what it is superior depends on the author (it allowing transfiguration alone probably isn't all of it).
I would say that the best idea is that wands, by allowing greater focus, make magic easier as well as opening the possibility for more powerful spells at the high end of the skill spectrum; basically, they're the magic equivalent to a gun.
After all, the original guns were significantly inferior to the bows available at the time, but the difference between "it takes a few months to train in their use" against "it takes whole years" was enough of a game changer to make gun proliferate and be improved upon until they surpassed everything else. And it works very well with the "imperialism is the reason" for why other magic cultures are much smaller in number across the HP world.
This also matches well with canon; wandless magic isn't impossible there, but only a handful of people are capable of using it, and even those only in particular way. Furthermore, magic like Expelliarmus, the cruciatus or the killing curse needs to be "directed", for lack of a better word, in order to actually strike a target. Plus, using a wand would probably make magic more powerful; there are hint of this in how Snape was able to use Legilimency without a wand, but used one when training Harry. In fourth year Crouch mentioned that it wasn't enough to reach the correct emotional state and know the incantation to cast the killing curse, it also needed power that the fourth years wouldn't have; that implies that a certain amount of magical power could be a prerequisite for some of the more advanced magics. In that optic, it isn't unreasonable to believe that wielding a wand works as an amplifier, especially since the Elder Wand provides an example of a situation where a wizard knew the spell and was able to cast it with other wands, yet the spell didn't take, but when cast with the Elder Wand, it did. If all wands worked like that, to a much lesser extent, it'd go a long way to explain their proliferation.
So... yeah, I think the best approach would be "wands are the magical equivalent to guns"; after all, guns were the deciding factor in the successes of the imperialist powers, so the idea tracks with what
@veekie said. And it's not like sword and longbows are any less lethal today than they were a thousand years ago (if anything, we're likely able to craft more deadly ones with our advanced technology), it's just that it's a useless hassle to waste the time required to train in the use of either since, if you're ever in need of a tool for killing, guns are sitting there, just waiting to be picked up. I think it would map to it really well.