Traversal in Zelda is not a necessity. The designers could have easily made a game which was just dungeon after dungeon without any traversal in-between. It's a design choice.
The space in-between the dungeons is not just a path though. Stringing just dungeon after dungeon is not a viable alternative. Getting to know the environment, exploring it for secrets and applying your skills gained in the dungeons to open up new paths are relevant gameplay mechanics in Zelda games, that go way beyond simple traversal and are well done. Due to that set-up some traversal between dungeons must happen though and I don't think it is too important, whether the pure act of moving from A to B in Zelda is very enjoyable in itself mechanically, as long as traversal time is reasonably short. In games where more traversal is needed, more sophisticated traversal mechanics are given, like in Majora's Mask the Goron mask an the Zora mask, which do ensure that traversal is fun in itself.
Whether or not some gameplay mechanic is necessary, though, has no bearing on its quality. And calling Zelda's traversal average is being overly generous to some of the LoZ games like Spirit Tracks.
If a mechanic is just there to enable transition from one main challenge to another in a reasonably short time, while giving room for additional enjoyable means of interaction, then it does matter, because it's dumb to compare the main mechanics of a game with what essentially is level select in the other. Note again, that the notion of level select is strictly speaking of traversal in isolation, environmental puzzles and exploration are not subsumed under this, although they are (among presentational reasons) the justification for
having the necessity of traversal.
The speed of the combat in Dark Souls changes based on the weapon used and there's plenty of weapon variety (not true in Zelda).
The speed of the combat in Dark Souls (speaking about 3, the only one I know) is low even if you choose the fastest configuration possible. Which is what I have done and I still found it unbearably slow and clunky. The fastest attacks in Dark Souls 3 are about as slow as the slowest ever in a Zelda game (Goron punch). Yes, Zelda does not have that huge a weapon variety. Considering its focus is on figuring out how to be able to defeat the enemies rather than variety in execution, this is a reasonable (and personally, preferred) choice.
Weight matters for swing speed and strength of the attack in DkS (swinging a great sword is very different than swinging a straight sword), not true for Zelda (toon link swings the Skull Hammer effortlessly).
This is wrong. The weight of weapons does make a difference in Zelda. Even from the early 2D games on, a hammer strike takes more time than a sword slash. Using the Biggoron sword also takes more time than the master sword in OoT. It does not get as slow as Dark Souls, but that's a design choice [that I absolutely prefer], not an oversight.
Enemy patterns are integral to fights in DkS, not true for Zelda (because enemies don't pose real threats even if timing matters).
Enemy patterns are integral in Zelda fights, though I agree that Zelda fights are easier than Souls fights. However, figuring out how to defeat enemies is even more important in Zelda than it is in Dark Souls, because in DS, even with a bad strategy, if you know all the patterns and are skillful, you will be victorious, in Zelda, you are required to figure out the weakpoint of the enemy or you will deal absolutely zero damage.
Different strategies and playstyles can be used to approach the same enemy fights in DkS, not true for Zelda.
True to an extent, though sometimes there are several possible strategies in Zelda. This, again, has to do with the fact, that Zelda has a different focus in its fights, which is not the pure mechanical skill, but figuring out how to deal with an enemy. Zelda is a puzzle-solving game, even in its combat, whereas Souls is a skill- and resource managament game. One may prefer one over the other - I'd not take another Souls game even if offered for free, you obviously prefer the Souls style over Zelda's, but they are not directly comparable and one approach is not inherently superior to the other.