...or make them "fighter specializations" like there are wizard specializations.
Actually, I'd be inclined to go the other way. If I were rewriting 3e, one of the first things I would cut would be the Specialist Wizard rules. Instead, I would have two feats:
Lesser Specialisation: gives the +1 to save DCs from the Spell Focus feat, plus the +2 to Spellcraft checks that Specialist Wizards currently get. (Replaces Spell Focus. And a character can only specialise in one school.)
Greater Specialisation: grants the +1 spell/level/day currently gained by Specialist Wizards. (Requires the corresponding Lesser Specialisation feat.)
I would also be inclined to turn Summon Familiar/Improve Familiar/Greater Familiar into a feat chain.
(I would also adjust the Sorcerer so that the only difference between Wizard and Sorcerer was the different spellcasting. So, the Sorcerer would get the same Bonus Feat progression. I believe they already have the same skills, BAB and save progressions, and familiar progression, so that's a minor change.)
The original Fighter class of early D&D created a bunch of spin-offs, the problem being that each of them is always quite rigidly defined, with several "signature" abilities (not normally available to others) but then only little flexibility.
It is the same as if there was an Illusionist class, an Evoker class, a Diviner class etc. and illusion spells were available only to the Illusionist, energy spells to the Evoker and so on. And the Wizard class had access to just the generic spells like Detect Magic, Dispel Magic and other spells that don't fit strongly into one category, but then again making all this generic stuff also available to the spin-off specialists, with the only difference that the Wizard would have more of them.
Yes, exactly. Indeed, the Psionics rules do exactly that, although there are a lot of 'generic' powers and relatively few 'specialist' powers. Indeed, it's not entirely out of line with the Cleric's Domains, as well, although those tend not to give unique spells.
But playing a "versatile" Wizard is an absolutely valid choice, and in fact it's possibly been the most wanted type of Wizard PC in D&D, hence we rather get a Wizard class that has access to ALL arcane spells, and specialists are in-class options (like schools or traditions) plus occasionally also a spin-off class but only a few years after the core is published.
Indeed. WotC (and Paizo) are now in something of a tricky position - Wizards and Clerics have access to this
huge range of abilities, and any measure to reduce their access would be met with massive resistance (because nobody likes losing powers). The consequence is that there really isn't much room for more specialised spin-off classes*, or even variant 'magic' systems such as Psionics or Incarnum - pretty much anything they could do is something that one of the other classes can already do, and at the lowest level where it might be considered balance.
* That said, I
really like what WotC did with the Warmage, Beguiler, and Dread Necromancer, at least in concept.
One way to deal with this problem, is to just have one Fighter class in the game, and make Paladin, Ranger, Barbarian, Monk, Swashbuckler into subclasses/specialists based on "feats" or "manuvers" (or else, doesn't matter at this point) that the Fighter can anyway access. There can be exceptions such as feats/maneuvers exclusive to one of those subclasses, but not many just as there aren't normally many (in fact, any!) spells unavailable to the generalist Wizard. Or there can be unique features associated to each subclass just like there are now for each wizard tradition.
My preference would be to
not have unique features, but rather to grant the specialist either earlier access to 'signature' abilities, or simply to grant them
more such abilities - the same way that the Wizard specialist doesn't get access to specialist-only spells, but does get more spells per day.
I would also prefer to keep the Paladin and Ranger (and a potential Mageblade) separate - these classes are effectively hybrids with one of the spellcasting classes, and I think there's considerable merit in keeping that distinct. Unless, that is, you have a strong enough multiclassing system to make such a thing redundant.
(Of course, the problem with all of this is that before you go too far you're already into heavy rewrites of the system. Unfortunately, there are enough areas of 3.5e that I find problematic that if I were going to invest that much effort in house rules, I would be sorely tempted to just rewrite the whole thing instead!)