I disagree. Wobbling allowed at nationals but banned at locals defeats the purpose of learning the complicated grab follow trees and the tight inputs for ICs' punishment game as a developing player. Why bother learning this crap if it's all going to be obsoleted by something that's basically strictly superior? Moreover, you're not preparing them for the field that they're going to have to face, which can only be detrimental to their development.
I think we should just ban the technique since it does lead to degenerate gameplay, just not at high level. And even with that said, I feel it slants the focus of what people need to be good at by placing a huge premium on technical perfection because of the nature of the technique. No other technique auto-deaths you in the game as reliably as wobbling from a single error. I say, "single", because the technique is non-interactive once the opening is procured, which removes a huge aspect of the defensive game. Even when Armada hits a Falco with dash attack, Falco actually has a lot of options to escape the ensuing ****. He might die anyway, but he's given a lot of opportunities to play around Armada's combo decisions through DI and interacting with the stage with the trajectories he's ultimately dealt. This is huge and adds tons of depth to Melee. Wobbling does the opposite in that once it hits, provided the IC doesn't mess up, you're dead and you had no say in it.
I don't feel the persistence of a technique like this is healthy for the game because of how far and away it is from the rest of the game and how it adds so little. In fact, wobbling actually takes away from the game by hyper simplifying their grab game because everything winds up revolving around setting up a wobble if Nana is alive and within some semblance of being synced or going to be synced shortly. I feel this detracts from and further polarizes the stage positioning games that occur in matchups against ICs.
I feel that ultimately wobbling takes more away from the game than it gives it. That said, I also understand it's a pain to ban because it's not very well-defined and so forth. So we'd need to define it, decide on some semantics regarding other infinites they can do (blobbling or whatever the blizzard version is), and decide on what course of action should be taken.
On a side note, I find it ridiculous that people want a new tier list when we haven't decided whether or not ICs' best grab combo (and the best punish in the game by far) should be legal as the norm. These kinds of things matter a lot. They change whole matchups. And stuff.
My two cents.
I'll be honest, I find your concern with emphasizing technical perfection a bit hypocritical. You accuse wobbling for making players focus heavily on not missing L-cancels because if they get grabbed, they will probably die. In the very first paragraph, however, you mention that when wobbling is banned, players are required to execute complicated "grab follow trees" and "tight inputs". Surely you can agree that wobbling being banned puts much more focus on technical perfection, not just for ICs mains performing handoffs and dthrow-dair CGs, but for players trying to SDI out of dthrow-dair CGs. Strangely enough, I usually hear people argue wobbling should be banned because they WANT to increase the technical requirements for a KO. Most people think that as long as something is technically difficult, it balances out how strategically difficult it may be. Whether you agree with that or not, I think everyone can agree that we should not go around banning stuff solely because it is powerful unless it becomes an overcentralizing aspect of the game. Doing so would surely make us no different than the traditional school yard scrub who calls a good move "cheap" and cries whenever someone uses it against him.
Your other main point is about interaction between players. You say that during combos, players are able to interact, and this is a key part of what makes Melee's skill gap so huge. I don't think anyone could possibly disagree that constant interaction is a great aspect of Melee, but what actually qualifies as interacting? I think most people would define it as being able to influence the game so that there are multiple scenarios of any given situation. Ness's bthrow may be guaranteed to kill at certain percents, but the opponent is able to influence what trajectory he will take to his death. What about if the opponent is at a high enough percent that Ness can pummel 3-4 guaranteed, and he needs the extra percent to guarantee the KO? Let's consider this tactic Nobbling (because LOL). Once the opponent's at a certain point, Nobbling is a guaranteed kill, and the opponent is completely helpless. Is the opponent still interacting? No one in their right mind would suggest banning characters from pummeling at high percents where it's impossible to mash out, especially poor little Ness, whose grab range is smaller than [insert dirty joke here]. The only difference between Wobbling and Nobbling is (besides a \) that the ICs can pummel indefinitely without the opponent interacting whereas Ness can only pummel for a few seconds before executing the actual KO portion of the tactic. You may say that this difference in time means everything, but what if Sakurai went mad before releasing the game and decided to make ICs' second pummel do 100% as long as Nana was synced. As you can imagine, ICs wouldn't play any differently in this imaginary version than they would with wobbling legal in the real version. ICs would still get a guaranteed kill off of synced grabs as long as the opponent was at a high enough percent that they couldn't mash out before the second pummel.
The point of this theoretical version is to prove the point that the interactivity of wobbling is viewed differently solely because of how long it lasts and how boring it looks. People see robotic repetition that is impossible to escape and immediately consider it undesirable even compared to an alternative where the result is the same but it happens swiftly instead of sluggishly. If ICs did a simple two pummel-fsmash to finish off stocks, people would still consider it ruthless, but they would just say, "damn, ICs have a really good pummel." No one would view it as some sort of individual tactic that can be banned or legalized like wobbling. Conversely, if you made it so when Falcon kneed someone the game froze and the Falcon player had to tap A 30 times before the game resumed and the knee killed you, people would complain that during
all that time they were unable to interact with the game (or they'd scream their heads off with hype 'cause it's Falcon, but you get the idea).
It's easy to look at wobbling and say it limits interaction, but when you start to view ICs' grab as an actual KO move like Falcon's knee or Marth's tipper fsmash, suddenly banning it doesn't make much sense. Criticizing the inability to interact with a wobble is just as absurd as criticizing the inability to interact with an off-stage knee. They both kill you, and you need to just accept that your chance to avoid getting killed by it was a split-second ago when you got knocked down and tech chased by synced ICs or DIed Falcon's dthrow into a dropzone.
I would also like to remind everyone that we have banned a lot of stuff not because it was or is game breaking or overpowering but rather because it didn't fit subjective criteria that we decided tested skill within this game in its purest form. We got rid of Rainbow Cruise, for instance, largely because of how much the stage's design (side-scrolling level that runs along a track) affected the positional games of characters. Suddenly, the level obligates you to move with a certain bias or else it kills you, no interaction with the opponent necessary. Brinstar was removed for a similar reason. These levels (and many others) were deemed unfit for competitive play overall because they took away options from the players and polarized gameplay. It was not simply because space animals or floaties were good there.
I do not see how wobbling is really that different. It removes the fundamental defensive option that almost defines Melee, and disregards a huge amount of Melee's skillset normally available to the defending player. It polarizes the game around not getting grabbed and makes technical perfection leading up to the grab attempt by far the most important trait someone can have in this game. Moreover, it allows no room for positioning to circumvent damage like with many conventional grab combos.
I might have this all wrong, but I feel if we remove stages that aren't broken because they don't fit the mold for competitive Melee, then I'm not sure why this technique should be treated differently.
Choosing which stages do the best job of determining a certain skillset is a lot different than choosing which tactics are allowed for the same purpose. It's along the same lines of the people that argue we should ban Luigi's misfire or Peach's turnips if we ban stages for randomness. I'm sure if you thought about your comparison you'd realize how they are not the same at all. Characters and the tactics they use are at the very core of the game, whereas stages are essentially the lens through which we view them. If you need a more concrete justification for making such a distinction, I think the fact that the game lets you disable certain stages but not certain characters, moves, or tactics should count for something.