Some points worth adding though:
You can blame the old fans for gobbling up sh*t, but I think a larger problem is the new generation of mainstream gamers.
The fact of the matter is that when "games were for nerds", the crowd gaming was smaller I.E potential customers less, and with that comes a larger responsibility on the part of game-developers.
You can't opt for a hit and miss strategy in a niche bussiness - Especially if you consider the cost of production versus the risk of failure.
Nowadays however, everyone and their mums dogs play video-games, and so critical demand is less, and potential customers have risen.
Like with how it's done in all other parts of the media industry, it's more economically feasible to observe the trend of the average and design your product with that in mind.
Since the amount of gamers have risen in total, and the quality-demanding, obsessive gamer type has arguably become a much less important force in the market, games will be made accordingly - Final Fantasy is no different.
The fact of the matter is that you can still go around the internet, and find tons of people that hugely enjoyed the newer installments in the series - pressumably because their standards are lower(or different) compared to the older generation.
A company, thinking in terms of profit, is sure to notice this. Why spend ages, and tons of cash creating a product appealing mainly to a smaller section of the possible consumer base, when you can make a product with less effort that will appeal to the masses anyways?
You see this trend clearly in the music industry - Why should the gaming industry be any different?
Sakaguchi leaving and money issues etc, has surely had some impact, but gaming becoming mainstream, and everything that entails, is probably the biggest issue in my opinion.
Another factor, in terms of Japanese games like FF and MGS, is the Japanese culture and their view of story telling in visual formats.
The fact of the matter is that, despite their tradition of developing great games carried mainly by gameplay, Japanese gaming history has tons of examples of a deep gap between gameplay driven media and story driven media(not saying it's always like this though).
In many ways, the new generations of games focusing on cut-scenes and only partially interactive scenes seem deeply rooted in the "visual game novel" tradition. Many Japanese "gamers" seem simply to be more interested in the story aspect, than the gameplay aspect. In light of that, it's natural to put more focus on this from a developer point of view, if your main objective is to make money, or please the masses.
In that way, the direction of MGS and later FFs are only logical - It's imaginable that a lot of Japanese developers have always wanted to present their stories in this way(more akin to interactive movies, than games), but have been unable to due to technological limitations. If you think FF13 was difficult to endure, imagine if FF7 was presented the same way, but in that era of graphics, and sound.
(This trend is even becoming true for the west to a certain degree as well - Consider the casual gamers approach to gaming)
IMO both these explanations seem more likely in terms of FFs decline, as these explanations branch into the issue with a lot of other titles from Japan(and the rest of the world) that have taken a turn for the worse over the years since the second half of the PS2 era.
Also -
Although I agree in your general assessment of the series, I can't find myself to agree completely with your view on FF12-13.
FF12, while a completely different from earlier titles, was a good game in it's own right(I agree that the story was weak though - Lack of character development, and long stretches between ultimately short and unfullfilling story segments left a lot to be desired).
I imagine that if they had dubbed it "Final Fantasy Tactics : somethingsomething" or "Vagrant Story : somethingsomthing" instead, the difference would make more sense, and less people would have complained about it.
If it wasn't passed off as a part of the main FF series, I'd easily have rated it an 8 or something to that effect. Giving it 7 or less just doesn't make sense when you consider the vast amount of RPGs that are 10 times worse, yet rated in the 5-7 range.
Same can be said for FF13 - Where it fails as an FF game, it shines as an FF interactive movie. Unlike FF12, I have gripes with the gameplay(or rather lack thereof), but not so much the story - I didn't like it personally, but to write it off as bad story-telling IMO is disingenuous to the extreme.
If you look at the FF series over the times, the quality of writing has undeniably become better with the years, regardless of whether we like the character or plots or not. Consider the more sums of money they have to hire professionals to write, edit, and oversee the story, the better it will be in technical terms.
There is a big difference with the totality of a plot, and the way which the plot is presented with dialogue(and or dubs).
If we imagine FF7 made today, for the first time, but fleshed out by the people who do the work on the newer FFs, there would be a large different, and most likely for the better, in its expression. Anyone who says otherwise is either blinded by nostalgia, or has no idea what good writing is to begin with.
There is a big difference been something being technically well written, and something being creatively well written.
A creative product I.E much of what is related to the plot etc will always be something difficult to judge except by the most subjective of standards because everyone have different preferences for how stories should unfold or how characters "should" react in a given circumstance. Many people for instance, jump on any story ending abruptly with the victory of the villain, and call it bad writing, - which makes no sense whatsoever.
Similarly, one-dimensional characters are instantly branded as bad, yet I've met many people through the course of my life just as stereotypical and flat as your average RPG character - So go figure.
Technical aspects of writing however are much clearer.
The newer FFs(FF12 being the one exception I guess, but it's obvious that they weren't trying to create a story driven game to begin with here) are all, as far as I'm concerned, technically better written than the earlier ones.
I still consider the earlier plots better than the new ones - But they aren't expressed as well. Some of the dialogue in the earlier games, if you read it out aloud, are formulated like sentences you'd expect to find in a book for 4 year olds, or basic grammar books for students of a new language - "I am so drunk now, my head hurts." and stuff to that effect.
That's not good writing.
Personally, I found the cast of FF13 to do the job of resembling actual people much better than say FF8, which arguably had some of the worst character expression in the entire series(not counting anything before 4, and 12) - The only character with the depth to be called believable in FF8, was Laguna.
But again, discussion on those aspects of a game is hardly productive - With the right angle you could probably bombard the sh*t out of any game you'd like, given the time and place.
For the most part, your post was a great read.