I agree.
In 3.X, yes you are right about the fighter.
After about 4th level, yes. 3.X suffered in its initial release from a lack of play testing at high level. 3.5 suffered from the fact that making money in the short term was seen as a more important goal than making a good game.
However, prior to 3.X, if you had good stats, arguably the fighter was the strongest class in the game.
Even in pre UA 1e the fighter was slightly weak - but had something subtle going for them. Fighters chould use swords, clerics couldn't. Which meant two things:
1: The loot table severely favoured the fighter (most magic weapons are swords, and I think only swords go up to +5)
2: Swords do more damage against big enemies, which is a stealth damage buff to the fighter as you level up and fight more big enemies.
There are a couple of important points you are missing. One of the most important of these is that the Fighter's saving throw table improved more steadily and to a greater degree than any other class. Another is that Fighter's benefited from high strength and constitution more than any other class until Barbarian showed up in the UA. The constitution bonus for non-fighter classes was capped at +2. This meant that it was nearly impossible for a non-fighter class to get enough hit points to survive a typical end game burst of damage. As such, there was very little option but to have fighter meat shields. While the cleric could in theory heal himself, he couldn't survive getting hit hard in order to do so.
The strength bonus to hit and damage for non-fighters was capped at +1/+3.
Post UA, they had weapon specialization which meant that they could pretty much beat down any monster in the game. Using something like a two-handed sword or a hammer of thunderbolts (with ideally gauntlets of ogre power), you had a character that was basically an unstoppable force. He was almost impossible to hit. He almost never failed a saving throw, and he conceivably could have more hit points than Tiamat if you really played him to high level. And fully geared up with a girdle, weapon, and gauntlets he could basically deal the equivalent of a meteor swarm's damage to a target every round - hardly anything in the game could survive even a single fighter's full attack even if we ignored serious cheese like vorpal swords and intelligent blades with special purposes. Paladin/Cavaliers and Barbarians were really powerful and definitely competed in the meat shield slot, but Paladin's in particular would be a level or so behind fighters in advancement and really needed a Holy Avenger to outshine a fighter.
Additionally, we think of rogues now as skill monkeys, but when they introduced the NWP system it wasn't rogues that earned the most NWP's. Fighters were actually pretty well off in terms of secondary skills.
In 1e, fighter was not the weak link in the party. That honor belonged to the thief. Thieves never got good stuff. At low level none of your skills were reliable and as such a good thief player never used them unless he had to. A thief that relied on his find/remove traps skill was a dead rogue. But by the time you hit high level, your skills were trivially obsoleted by the application of minor magic - find traps, levitation, detect magic, spider climb, invisibility, silence, etc. You were reduced to the level of a henchmen, unable to contribute more than your player could contribute except in minor and non-critical matters. Basically, you tried hard to help your friends conserve their spells and hit points.
Next to the thief, the cleric was the least fun and effective class to play. You basically where a hit point battery that might have minor utility value. You had few spells, few ways to deal effective damage, and not enough hit points to stay on the front line anyway.
The ideal 1e party was generally one cleric to heal and raise dead if needed, one wizard for those times when the text of an adventure said something that amounted to 'cast forget or die' or 'cast stone to mud or die', and a lot of fighter types. If you had space and could keep one alive, add another wizard.
I personally feel most of 3.0's class design problems were overcompensation for the flaws in the class design of 1e. Fighters got gimped hard because every class to a certain extent took their stuff. Clerics and Rogues were deliberately designed to shine, and the shackles were taken off of wizards so that they'd be more fun to play at low level - resulting in them being severely overpowered at higher levels. It was clear the design was done by player's of 1e that knew what problems they needed to address but hadn't fully considered why 1e worked as well as it did.
Ironically, a lot of the best class design can be seen in multiplayer cRPGs where balance has to be taken really seriously and playtesting likewise is taken really seriously.