You seem to be confusing two issues. The Fighter lost Weapon Specialisation before they gained prestige classes, and with the major exception of Cleave (which is still present in the form of Great Weapon Mastery) the feats weren't all that hot. Twenty years ago fighters were at an all time low, encumbered by things like armour check penalties, by wands being cheaper and more common than magic swords, by feats being generally pretty awful, by iterative attacks coming out at below maximum BAB, and more. The 2e fighter could kick ass and take names - and had good saves and priority on the magic items table. The 3e fighter didn't.
The 2e fighter was simple - but at first level got +1 to hit, +2 to damage, and an extra attack every two rounds. Heavy weapons did more damage against large foes (which had far fewer hit points anyway). And had priority on the magic items table.
The 3.x fighter was a disaster. It lost weapon specialisation. It lost good saves at high levels. It lost priority on magic items because all its magic items were really expensive (when you can get three wands of CLW for the cost of a single +1 sword which do you pick?) It doesn't have anything like Second Wind or Action Surge. It couldn't actually make good use of the feats it had at low level if it wanted to prestige class as that would tie them up. Armour really got in the way. It moved from near top of the non-magical skills pile to the bottom.
Why would a 3.X spellcaster support a martial if they could have an aggressively hegmonizing ursine swarm (druid who turned into a bear, had a bear companion, and summoned bears) in the party and support that? And that was the problem with the "fighter as recipient of spells" - they soaked up party resources without providing any, while the ursine swarm provided some in return. It's not a model I want back.
What I want is a fighter who can (as in 2e and 4e) stand on their own two feet.
Eh?
3.X Fighters lost Weapon Specialization? What's this then?
You might say that's not a great Feat, but we don't even have this as an option in 5e unless you exclusively use a one handed weapon. Let alone the ability to upgrade it with Greater Weapon Focus and Greater Weapon Specialization later.
And yes, I didn't say the 3.X Fighter was good. I said it had several things that the 5e Fighter lacks. As to why a 3.X caster would support a Fighter, that's because it's more efficient.
I mean seriously, for all the talk about "CoDzilla", it takes a lot of action economy to layer buffs on yourself to become all powerful. Many buffs that could be put on the Fighter who could immediately use them! That there were good self-buffs at the time certainly helped cause the problem (and the misuse of Divine Metamagic), but the last 3.5 character I played was a Cleric who used DMM+Persist...to lay down buffs for the entire team. This left me basically using Reserve Feats for the rest of the day, but we were far more effective as a group than a single CoDzilla could be, and there was no need for any prep time.
But hey, I don't feel the need to argue that point- and I won't, since it's not relevant to the greater point I'm making here. Fighters have less than they once did. Most of what Wizards got was Quality of Life choices, and their ability to actually help support other party members effectively. Which isn't a nerf to them, but to everyone else!
The Fighter got a lot less in the transition. There is no longer any real dedicated design space to making them the master of a weapon. Everyone can use the same weapons the Fighter does (and if they can't, getting the ability is trivial). The same for armor. Everyone attacks the same as the Fighter.
The Fighter gets 2 bonus ASI's, has a lot less Feats to work with (if he or she even has Feats to work with), a badly scaling self heal, an extra attack routine (which again, is really just a patch for not being able to get Haste), and a laughable reroll of a failed save as a high level feature. Sure, you get 2 more attacks, starting at level 11, and that's not nothing, but it's not something they
gained. For everything Fighters gained in 5e, they lost something, even if that thing wasn't strictly bolted onto their class chassis.
But what about Weapon Masteries? Big deal, that's not a Fighter buff. That's a buff for anyone who happens to be a weapon using class.
In conclusion, caster's didn't really gain very much of note, if you really get down to it. But they gained more than they lost, and you can't say the same for all the non-magic classes.