There are a lot of questions here, perhaps too many to answer properly in 400 words, but my short answer is "Yes" to most of them.

What's interesting about Academy procedures is that they are actually more transparent than ever before - with sites like Gold Derby (formerly at The L.A. Times) now routinely analyzing the nominations, there are ways in which the nominating procedure has become public knowledge. Mind you, it's a public knowledge only for people who post on/read Gold Derby, but it allowed for recent changes (like the shift in 2006 to Blue Ribbon Nomination panels and then the shift BACK to popular vote-based nomination systems after the results only drew more criticism) to be discussed/dissected/debated in a public forum.

I'd definitely agree that the Emmys serve as a reflection of broadcasting history, and they absolutely played a key role in the rise of HBO's quality brand in the early 2000s. What's interesting about HBO and genre, however, is that they rarely refer to their own shows as dramas or comedies outside of the context of awards, choosing instead to refer to them as "HBO series" (likely to further distance themselves from this pesky "television" thing they want to disassociate themselves from). So on some level, the Emmys are the only reason HBO has to make the distinction, a distinction they actually draw on the half-hour/hour long binary in most instances (outside of exceptions like In Treatment, which is really 2-2.5 hours long if you factor in each week's episodes as a whole).

I do think that, without generic categorization, many shows would fall through the cracks and certain inequalities of the Emmy system would be revealed. However, there are always inequalities in any award system, and I think you're right to ask whether this is the main one of concern. What I'll say is that this is one of the most visible: flipping through nominations casually, or watching the broadcast without following the nominations, strangeness that manifests within the nominations (as opposed to absences) live on throughout the process and draw the eye to further concerns (including many you mention).

(One last note: I didn't have time here, but I'm also interested in shows that have CHANGED categorization - Gilmore Girls, for example, submitted in drama in 2007, but submitted in comedy before then.)

To your first point, it will never happen so long as the networks are the ones airing the awards. While the network/cable split might ensure that big network shows might win more trophies, it would also suggest a hierarchy between cable and networks that shows like The Good Wife are trying to break down. I think that everyone involved wants to play down that hierarchy as much as possible, as it plays into HBO's desire to be separated from the networks in the public consciousness. CBS might actually be the one network who wouldn't object, given that Viacom could compete in both categories. I definitely think a Premium vs. Network/Basic split would be out of the question, but even a Network/Cable distinction would raise alarm bells for executives.

It's tough to know how, precisely, the panels operate without actually being in one of them. It's just incredibly awkward all around: not only are they watching performances that can differ generically, but some are longer than others, and watching them back-to-back-to-back creates a really interesting comparison point. Which one comes at the end of the day? Which one comes in the beginning? If voters haven't seen the programs in question, which is entirely possible, will they not have had access to the other materials (promos, for example) which help mediate their impression of a program's genre? The panels are not a typical audience, nor do they represent a typical circumstance, so generic classification might be even more complicated in that context.