Most of this is gonna be about BotW, because that's the one I played, but TotK seems to have gone a little ways to smooth over these issues.

I would say that maybe number 3 is the only real point there. Most of the other things that it "solves" are "problems" that are created with the weapons system in the first place. Like number 4, that's not a problem with the alternative of a weapon that doesn't break, like what happens in the other games. The difficulty scaling could've just been done by the devs with a basic, regular master sword style thing, like what existed in the other games. It doesn't help balance at all, is what I'm saying. I would say, precisely because the weapon system exists, there's actually less balance in this game overall than pretty much every other zelda game to date.

Some of the harder enemies are more likely to appear in different areas, and so entering those areas with low tier weapons means that the weapon system kind of acts as a mild gate, right, in the sense that you will go down to a one hit KO and be able to do no damage. Sidenote, but if this were how the game really worked, it would actually act against point number 4, since you wouldn't be able to surmount those areas without properly scaling up to take them on, and going and farming the weapons in some other area which is a "lower level". This gating is especially true of the castle town, more than almost anywhere else in the game, where it kinda happens more in discrete, singular locations. At the same time, most of the areas in the game, the overworld, level up their mobs to scale with the player's weapon rating, making the entire point moot. There's certain areas where higher tier mobs, relative to the player, are more likely to spawn, sure, but again, that maintains throughout the whole game and is totally relative to link's current character, which means they could've gotten away with a steady state, singular weapon throughout the whole game kinda deal. Basically, those areas with higher tier monsters, stay higher tier regardless of whatever you do. The only major exception I can think of is the guardians, and I'm pretty sure they scale to your level anyways, they just don't do it in visually distinct tiers.

The player playing dynamically isn't really incentivized outside of the immediate intro, because, as you said, most enemies drop weapons that are the same kinds of weapons you'd use to beat them, and later on the player can kind of be expected to have picked up enough weapons of a similar scale with the enemies. The thing which incentivizes the player to think outside of the box is the enemies being slightly harder than the player can be expected to take on and the terrain and scenarios in which they fight enemies to be varied and unconventional, which I have found to sometimes be the case, but again, isn't due to the weapons scaling. That's something the game could've been designed to facilitate anyways, the weapons scaling just complicates it.

So, uhh, yeah. I don't think the weapons scaling does much to help the game's design at all, I think it probably overcomplicates it while offering basically nothing in return. Maybe the continuous scaling until the end is supposed to offer some sense of power fantasy for the player, but I think that kinda stinks and is dumb, because the game is basically functionally identical, in terms of the mechanics of the pure combat system, basically all the way through. Outside of the immediate intro, anyways.