w00t, my first post here (and I'm sure I'll make a bad first impression 
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I must say that I mostly agree with what OP has said; the evidence from the way Squeenix has been taking FF in general, and FF7 in particular, since the merger, suggests that a FF7 remake will be disappointing for many of its older fans for the reasons given. I won't say whether the compilation or the recent games have actually been bad (although that's certainly my opinion), but they have received a very "mixed" reaction from fans; a lot of people are concerned about where the series is going.
It's true that Squeenix have managed to put out some rather nice remakes of the older games in the past few years, but it would be unwise to infer anything about a FF7 remake from those. They have been fairly small and unambitious (I don't mean this in a bad way) remakes of games that didn't have a big fanbase, they've been for handhelds and they've been expected to get rather modest sales by FF standards. They've also been remakes of 2D games rather than 3D, so it's been much easier for Square to make the games seem like a major revamp without doing anything that would alienate anyone but the strictest traditionalists. Just making them 3D changes a lot. A FF7 remake would almost certainly be very different, since it would be aimed at a much broader market and would be expected to be a game that pushes everything to its limits.
I feel that, for the purpose of argument, we should take the saying "room for improvement" literally 
FF7 is, we can all agree, one of the most beloved games ever made (it's also one of the most hated). Whether that means it's actually one of the best isn't important; what matters is that it's the best in a lot of people's minds. This means that, for those fans, there is very little room for improvement. When there is plenty of room, something can be improved quite easily, but when there is little room, it's much harder to improve things and much, much easier to mess things up; one has to be very careful when everything's in a delicate balance. Squeenix will have to be careful as well, if they want to avoid pissing off a lot of fans.
It's certainly true that any major changes in gameplay are likely to incite a bloody uprising amongst traditionalists (although I would cream my pants if Squeenix remade the game with a harder difficulty mode), but there are even risks to tweaking the things that most people would think have the most room for improvement. Redoing the graphics isn't as straightforward as it might seem. The graphics in the Compilation, and especially in Advent Children, have been much more than a simple upscaling of the original game's graphics; there is a very different change in visual style. The male characters are a lot more feminine looking, Tifa is a lot more "natural" looking and the colour scheme has changed from psychedelia to black & white (I think, and I know I'm not alone in this, that the deep rich colours are one of the things that made the original special; they make the feeling of the game much "warmer" and make the world seem very "alive", even if they aren't very natural). Squeenix would also have to choose between keeping chibi characters and using normal sized ones (and we all know that they'll choose). I spend most of my forum time at a place where improvements to FF7 are discussed quite a lot, and there's actually a quite even split between people who like the chibis and people who like the proportioned models. This isn't just nostalgia either; humans are programmed to empathise more towards cute things, so it would make sense if those silly looking characters actually made fans connect more strongly to them than normal ones would have. Of course, there are some people who don't feel that way as well. Anyway, there'll be controversy with whatever choice Squeenix make.
Now, let's say that Square actually did manage to keep all of the fans happy. Let's say that they kept everything we love about the gameplay and made use of technology to give us options with the graphics (such as whether to use chibi or full sized models, in the same way that some games let you choose how much blood there'll be) and the sound (such as whether to have English voice acting, Japanese voice acting or even none). It won't happen, but let's pretend it might. Here's where it goes into hard mode for Squeenix: the critics would hate it for not being innovative enough. Srsly. Critics and fans often look for different things in a game; the 40/40 that Famitsu gave to FF12 shows that. If Squeenix made the perfect remake from the fans' POV, it would be panned by the critics.
I think that my post has deviated from its original point (was there an original point? ), and is already very tl;dr, so I'll just sum everything up by saying this: whatever Squeenix do, someone is going to be disappointed, and if they try to avoid disappointing anyone (which they probably will), they'll disappoint everyone. I actually feel quite sorry for them in a way. 
Essay Pro