clearstream
(He, Him)
We might be in greater agreement than appears on the surface. Here you point out that melee has better defense or (ignoring CEx/SS silliness) does more damage, or both. A direct comparison could be a Defense style, sword-and-board Battlemaster, with an Archery style, longbow Battlemaster.melee either has better defense or does more damage or both when compared with ranged. Melee has that advantage as well as the advantage where damage is more likely to be spread over more party members than concentrated on fewer.
...typically melee characters do more damage and have more defense than ranged ones.
Sword-and-board will have +3 AC over the archer, all else being equal. Their damage is approximately the same, ignoring feats. Same number of attacks, same 1d8 die for the weapon. This would seem to assert that +3 AC = 150' range. It is clear then that damage + range is worth more than damage alone. As well as +3 AC, the melee doesn't suffer disadvantage when in close. So the ranged damage, compared with the melee damage, is compensated for twice.
This implies that ranged is worth more than melee; and perhaps your point can be restated that, generally, in 5th edition, melee characters enjoy benefits the make up for not having range. I think also, we have a decent handle on just why ranged is worth more than melee: reach, up-time, target selection, mitigation of return attacks.
Do you see what I mean? For me, it justifies looking hard at a feat like Sharpshooter which, even when not in conjunction with Crossbow Expert, can put ranged damage above melee. Agonizing Blast, on the other hand, is a very good attack, that overshadows other options for the Blast user, but it does not overshadow melee damage.