This is more like, "Why does Final Fantasy Suck Now [if it was ever good]?" than, "why sequels suffer". If you're going to pick X as the point of departure, I'll just fall back on the common belief that SquareEnix ruined everything (IX was Squaresoft's last FF game).
But just because I don't completely understand what you're getting at, let me pick at your main statement:
Final Fantasy, I believe, is no longer Final Fantasy. I believe that Final Fantasy was all about exploring dungeons, going to towns, getting lots of weapons and armor, playing mini games, and have a simple turn based battle system. That's what it was like up until FFX, then they changed it all, and look what happened. We no longer have stories about the characters growing from some "I don't want to help nobody" asshole to "I'll die saving this planet".
1. All about exploring dungeons
-FFXII had dungeons in spades
2. Going to towns
-FFXII had tons of towns, the biggest in the franchise
3. Getting lots of weapons and armor
-This is every FF game, except for FFVIII. I wouldn't call the reduction in redundancy of weapons (beginning with FFVII) a bad thing, considering they largely only affect your attack and hit% in FF games, but whatever. Consider this the same as the streamlined inventory between Mass Effect 1 and 2.
4. Playing mini games
-Not many mini games in I-V, or XIII, the rest had a bunch
5. Simple Turn-Based Battle System
-This ended with XI (and by extension, XII). FFX's battle system was not only simple, it was revolutionary. It's one of the few JRPGs I can name where your vanilla attack is NOT always the best option for defeating enemies in a timely manner. Up until that point, it was 'equip the best weapons, grind your attack stat, use attack -> win'. Any deviation from this pattern would cause you to lose turns, time, health, and eventually, the entire battle. 90% of magic spells were useless. On the other hand, FFX actually gave enemies specific status weaknesses in addition to elemental weaknesses, the effectiveness of which were increased over 2-fold, so that it was smarter to blind a bunch of flying enemies and throw lightning at them than it was to constantly mash 'attack' with your heavies. But I digress, most people can't get past the story, inability to skip cutscenes, lack of a world map, etc. etc.
6. Story (?)
I don't know how you concluded that a change in gameplay resulted in a change in story development, but look no further than Motomu Toriyama and Daisuke Watanabe, who led the scenario and script writing on X, XII, and XIII (while their roles were minor or non-existent in previous entries).
Basically I think your argument boils down to, "Final Fantasy XIII is terrible", and I agree. The battle system is actually pretty fun and entertaining, but you don't really get to use it until you've crawled over 40 hours of absolute garbage. Then the game becomes a real Final Fantasy game, albeit without interesting environments, the ability to use all of your characters, and any real goal other than some mediocre side-quests. I chalk all this failure up to the inability of Japanese developers to utilize current-gen hardware. FFXIII feels like they spent more time on the graphics than anything else (and the graphics aren't even
that good).
But whatever, a lot of people made the same exact arguments when FFVIII came out, and now it's regarded as a classic. For those who were still upset by VIII, Squaresoft created IX, which was a big throwback to the SNES titles, as well as homage to the entire series, including VIII. SquareEnix's problem is that they never really responded to the ire of fans after XIII. Instead they took the G.W. Bush route and said, "We can either admit that we screwed up, or stick to our guns and make things worse. Because sticking to your guns shows character, and people would rather have character than quality." Of course now there are FFXIII fans who were pissed off at FFXIII-2, which, in an uncharacteristic gesture, SE is apologizing for with yet another sequel. But this is another digression... I've stopped hyping myself up for each new entry, at least until they give up on all the Ivalice and Fabula Crystal whatever crap.