I don't think specialization being the dumping place is up for debate. The manga has literally said that specialization is where you throw in nen that does not fit with the rest and is not a real category.
The only way for the parasitic nen to be "conjured" would be that they are conjured as invisible and whether such a thing is possible is debatable at best. It does seem like in is enough to see the beasts in which case they should be emitted and presumably sticking to their host. That said, you can't "transmute" a pot. Transmutation is specifically changing the quality of your nen, it does not apply to physical objects. You could manipulate an object, enhance it or even use emission to impose nen on it. But transmutation does not apply at all.
I don't think the armor you suggest would be close to enhancement. You would take nen, shape it into an armor and then simply place it over something. That is all around simple emission. If instead of an armor you used it as a long range shu then it would fall more in line with enhancement though emission would still be the more significant factor in it.
It is true that there are no nen scientists as far as we know but I don't think the martial arts thing works as you say. When it comes to how nen functions the manga is very consistent across the board. It's not just martial arts with mythical explanations if the evidence we have suggests the explanations we have work that well and consistently. The exception would be specialization due to how it was defined early in the manga.
The manga did not say that. It said that in the water divination test, everything aside from the 4 other principle's results is specialization.
My reasoning still stands that it is in fact as real of a nen category as the others because specialization user still have deficits and benefits as usual in the nencycle (so a specialization user is always opposed to enhancement and never, for example, inbetween conjuration and emission).
The nencycle itself is a bit shaky. For example, you can become a specialization user later in life. That means that the water divination test and the nenclasses in general are more rough estimates than something really strict. It is even said that a user can exceed the limits of his category or another if he trades in other deficits. All in all, the nenclasses are about patterns which get grouped together.And specialization users can only be logically included into the nencycle at the place they are. If they were really just a dumping place, there have to be users who are specialization but lie on other places of the nencircle, and it would not make sense then that conjuration is 40% away from manipulation instead the usual 20%. That is only logical if in fact there is a whole category between them.
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I think the martial arts explanations are 'mythical' in some ways. For example, the oath mechanics is never explained in detail. It seems to be more of a result of meditation and looking what works than anything else. It is not a case study as scientist would do it, checking exactly which limitations and oaths work and estimate how much they strenghten an ability by countless of case studies, checking brain and nenwaves and getting close to completely understand that mechanic.
The same goes for 'nen staying behind'. I think there are a lot of things which rather become legends and mystical knowledge than well studied subjects. For example, it is obviously possible in some circumstances for a 12 year old kid with to exchange his talent for shortlived superpowers.
It would be very interesting for a scientist to look whether this can be replicated. Sure, not everyone is as talented as gon and it took trauma. But it's not like it is out of question to replicate this effect to some extent, maybe being able as an enhancer to sacrifice lifetime and talent in order to slay an important enemy.
But there is no scientist and the only people who even know about it are gons friends. Other hunters will, if anything, ehar legends about it being possible. The same really goes for hisoka's nen ressurection.
So ya, i think tha in-universe, the nen explanations and models lose some rigour once you look into the finetuning and the genius applications of it.
I do not see that as a flaw of togashi's writing, because it makes absolute sense when you think about the explanations being given by martial artists.
They are pretty good for learning nen and having an emotional understanding of it, which is more important for users than understanding it in scientific terms.
That being said, some nenabilities might also be beyond just simple categorizing. After what i have said before, i think 'parasyte type' is a rought term for nenabilities which require a host. Maybe even abeganes ability could be categorized as such.