Did you read the article on HITH and HLLE? It was not written based on a couple cases I have seen or by limiting myself to what the books say, it was written based on talking to many people who have first hand and varying experience with it. That is exactly what science is. Using as many cases as possible and not limiting yourself to previous findings and commonly held beliefs. I looked at the cases and made the simplest conclusion possible. HLLE seems to be a symptom of many problems (like dropsy) not a single cure and cause disease (like ick).
It explains how when all cases are taken into consideration a single cause and cure is extremely unlikely. It seems there are MANY causes of HLLE. Otherwise it would not be so debated and would be better understood by now. People want "X causes HLLE", but the evidence shows it is more like "A, B, C, and D can all cause HLLE".
There have been multiple cases where HLLE developed while carbon was in the tank. The carbon was then removed. Then the HLLE went away. When carbon was returned, so did the HLLE. This is an undeniable link between the carbon's presence and HLLE. These are not cases where carbon was removed along with adding meds or changing anything else, more of a last ditch effort of trying different things and carbon was the only change at that time.
It has definitely occured in many tanks without carbon. And very few cases seem to have carbon as the main cause. But it has happened so there is a risk there.
Actually most do not believe it is bacterial. HITH has been linked to certain parasites (Spironucleus vortens and Hexamita spp.). HLLE seems to not be caused by any pathogens, but has an array of possible causes. These range from dietary problems and deficiencies, water parameters, water quality, and even carbon (most likely the carbon removing certain vital nutrients).
I have seen it in multiple books and cited by multiple very advanced aquarists. Go on to a forum all about reef keeping or planted aquariums and ask about carbon, they will provide examples and many if not most will not be using it for the reasons stated. You obviously won't take my word on it, so talk to many other aquarists and let us know what you find.
I am not sure what all carbon will remove, do you? I have not seen studies stating it does absorb Vitamin K, but not Vitamin E. But the results people get when using and not using carbon support that carbon does not just absorb the bad things, but many good things as well.
Have you found any studies that show that carbon only selectively removes medications, discoloration, and odor? If not then you can't assume that is how it works, especially with evidence to the contrary.
There is no need for carbon use in the aquarium at all unless you need to remove medications or have some rare problem with your water. This is very well proven by all the people who do not waste money on carbon and their tanks are doing better than when they did use carbon. If you will only accept well supported and scientifically proven theories, then there is very little you can do in fishkeeping. If you want to go by what others have learned by using different methods than those that have always been used, by thinking outside of the box, and questioning the habitual methods, then do some asking around and see what you find.
Did you read the article on carbon? I know I am not a published author (in print), or a leading scientific researcher in any field. But they are written from experience and based on facts. Keep in mind most articles are written by advanced hobbyists, not scientists. There may be more helpful information there than you give it credit for. Don't unquestionably take it as undeniable fact, but as another possible resource for a little bit of decent information.
