No. The problem is people not using certain specialist ways to play the wizard. The wizard playstyle that's the problem is what I consider the default one. There are two basic wizard playstyles: Blast Mage and Problem Solver. If you play as a blast mage there is no problem. If you play a wizard thinking "I'm smart. I have magic. How can I make this challenge easy or this enemy almost irrelevant." Then you have problems. And to me the Problem Solver style is the default.
The problem goes waaaay beyond a few spells. And involves both legacy D&D problems and a whole lot of problems from 3.X. It's not just a few spells that need nerfing. It's an entire conceptual overhaul, and undoing about half the changes made turning 2e into 3.0.
A high level wizard was known to be more powerful than a high level fighter and a low level fighter more than a low level wizard. This was a problem in itself but one that was accepted and understood. The fundamental problem levelling is that the fighter basically gets better with a pointy piece of metal, whereas the wizard gets both more spells and more powerful spells. And a lot of those spells are about ways to make people waving pointy pieces of metal irrelevant.
At about level 10 (depending on class) the published game entered the endgame. Your hit points stopped rising and you gained either a tower for a wizard or land and an army for a fighter. This was about the point where the wizard left the fighter in the dust anyway. Note that 3.X removed this cap.
1e wasn't balanced.
Which is why Gygax added Specialisation and the two commonly thought to be overpowered fighter variants in Unearthed Arcana - I can dig up a link where he agrees with this if you need it. 2e kept the fighter specialisation fix - but added specialist wizards, who gain massive power (at least 25% to the number of spells they can cast per day, and 50-100% to the most powerful spells) for a little versatility.
Problems added by 3.X
Note that this list is not exclusive to wizards - almost every problem I'm listing for wizards also applies to clerics and druids.
Hit point inflation.
The way Con is used has changed. Whereas a wizard would start with 1d4hp in 1e they probably start with about 6 in 3e. And monsters have many more hit points. To illustrate, a
2e Ogre gets 4+1 HD or 19hp. A
3.X Ogre gets 29 hp or more than 50% more. So it takes half as much damage again to kill an ogre in 3e as 2e. But Fireball is doing the same 1d6/level damage it was in 2e so does comparatively much less damage. In playtesting this probably offset the spell count inflation. (Note: Ogres are simply the first monster that came to mind). Fighters of course have to go straight through the inflated HP.
And a wall of stone is a wall of stone. It doesn't care much about hit point inflation. Likewise any other spell to bypass or entirely render irrelevant the monsters.
Caster Versatility 1: Spell count inflation.
A decent spellcasting stat adds a spell per level. So a 1e 5th level wizard would have
one third level spell per day. A 3.X 5th level specialist wizard gets
three.
Caster Versatility 2: Free Spells for Wizards
In 3.X a wizard gets two free spells of his choice per level and starts off with about half a dozen L1. This is new and means that the wizard isn't dependent on the DM for spell selection. And can pick an entire pile of good spells.
Castger Versatility 3: Scribe Scroll (free for Wizards)
All wizards get Scribe Scroll for free - and scribing almost any scroll takes only a day - if you aren't getting the odd day off from adventuring you're likely to be suffering from PTSD. This means that you don't have to prepare spells like
Knock - a smart wizard can wander around with all the advantages of having a couple of knock spells prepared for the one day in thirty when the rogue taps out without it costing him any actual daily spell slots. (Of which he has far more)
Caster Versatility 4: Prep time
In 3.X a caster is prepared in an hour. Period. In older editions it took longer at higher levels. Much longer.
Caster Versatility 5: No Drawbacks
Haste used to age you by a year per casting. Hellloooo System Shock roll. No one cast that. Teleport used to go offtrack and potentially kill you. I could go on. 3.X took away almost all those backlashes. (Mordaniken's Disjunction being the only one to come to mind).
Saving Throw Changes 1: Homogenisation of difficulty by effect
If you convert AD&D saving throws into 3.X saving throws,
The save vs spell DC is about 17. But save or suck, being more powerful, is normally a save vs death magic or poison of DC14, or a save vs polymorph or petrification of DC15. This is a fairly significant relative boost to the effectiveness of non-damaging spells over damaging ones.
Saving Throw Changes 2: Inflation of DC by Wizards
A DC of 17 looks about right when converting the fireball save at L5. Level 3 spell, Int 16, +2 Int Item. Now. Let's say that we've got a conjurer who started at Int 17 and focusses in Conjuration. He's now Int 18 + 2 (or even +4). He's taken Greater Spell Focus (Conjuration) - if you're going to specialise in it anyway, why not? We're at DC20 and it's only going to rise with his level and with the spell level. A three point swing is a lot. And then the spell level goes up over time, so does Int, so does the stat boosting item.
Saving Throw Changes 3: Choice of targets
The wizard is once again confronted with our ogre. Who is big and burly. Turns out an Ogre has saves of Fort +6, Ref + 0, and Will +1. (The 2e Ogre had effective saves of +1 in all categories). With a save of +6 in Fort, the ogre saves against the stinking cloud from the specialist caster on a 14 - in 2e he'd be saving on 13. Here things have balanced out even with the optimisation. But this is a worst case scenario. Our wizard is going to remember that Stinking Cloud isn't the only spell on his list and instead go for Glitterdust. It's one spell level lower. So DC 19. But that means the ogre needs a
18 or he's out for the next five rounds, swinging wildly. A five point swing by using a lower level spell. Pretty hard to do in 2e.
Saving throw changes 4: The Fighter Nerf
In AD&D, at high level, the fighter had the best saves. Especially against death or suck effects. All between +11 and +13 - and he got there at level 17 which was four levels before anyone else capped out. In 3.X the fighter has arguably the worst saves in the game - only one high save out of the three (at +12), and the Rogue gets Evasion to boost his whereas the Wizard gets defensive spells. And with one stat being boosted as the character levels, the offensive stat is the obvious choice - meaning that the fighter's saving throws aren't going to get this boost when offensive spells are.
Non-Wizard spellcaster changes: The Cleric
The cleric gets nine levels of spells with Miracle at level 9. Previously the cleric got 7 and started casting later - also needing to prepare heals rather than convert to them. And can prepare from anything on the entire cleric list.
Non-Wizard spellcaster changes: The Druid
This class needs to die in a fire - or rather to be broken up for parts. D&D 4e broke it into three classes - all viable. There's the nature-priest healer with an animal companion and a little magic. There's the shapeshifter. And there's the spellcaster. The Druid was probably the worst case as it required almost no work to be broken. The animal companion wasn't as good a fighter as the fighter, granted. It didn't need to be - because if it was a brown bear and close to the fighter's combat potential, the druid could be a
second brown bear. And then the druid had a decent spell list, able to cast 9th level spells and with the Polymorph Chain.
So that's where the overhaul 3.X needed came from. A vast set of changes that stacked.