Angel summoner/BMX bandit is usually the first example people give of imbalanced PC classes, and I will admit I only played 3e off and on (I stuck with AD&D). That being said, what I've found almost exclusively in these scenarios is that certain parts of the game are glossed over in the favor of the caster. Notably things like preparing spells, components, and spell interruption. Even in 3e, you still can only prepare a limited number of spells (unless you were a sorcerer, in which you were limited in other ways on spell choice). There is no way a player can prepare the perfect spells for all of the scenarios in that session. Their PC simply doesn't have enough slots to learn all the perfect combat spells and interaction spells and exploration spells, let alone how would the player know what to prepare. Then even if they did, do they have all or the required components? And do the monsters ever attack him or her when casting a spell in combat to interrupt them? And how does the player know how many encounters are going to be expected (meaning, how do they know how many spells they can cast that encounter and how many should they keep in reserve due to the unknown)? IME, what I've seen is parties cater to the caster's needs even if it goes against the natural flow of the game. I.e., "Well, we need to rest because I blew all of my spells." If you're doing that, then no wonder casters seem so powerful, because you're placing them as more important as anyone else by catering to them. Not to mention another thing I see a lot: PCs being able to rest whenever they want, AKA the DM pausing the game world when PCs decide to rest, which shouldn't happen.
Having seen it first hand in 3E, when a Wizard gets to a high enough level, you're unfortunately quite wrong. They can be bad-ass enough that the only way for the DM to challenge them is to cheat - and usually put them up against another Wizard.
I've been playing since Blue Box Basic. Basically, if you ran a tight ship in AD&D, the Wizard really was a 'glass cannon' that had huge amounts of power that was significantly held back by long memorization times, finding spell components, ease of disruption of casting, scarcity of new spells, vulnerability to a Cleric flinging a 'Silence' sling bullet, etcetera. It was a wacky form of being completely imbalanced, but the game was an escort mission to protect this incredibly squishy person that, if every single person coordinated well, could turn the tide of combat. Usually.
3E dashed all of that. They eliminated all the flaws Wizards had because they were 'annoying'. You could take feats to eliminate the necessity of components or gestures or vocalizations. Abilities and feats were added so they were able to cast even while soaking significant damage. You could 'take a 5' step' to disengage from a melee attacker and cast without any threat. Spell memorization times were reduced to nothing. Casters gained spells of their choice automatically every level.
The way spells mechanics were built - the saving throw scaling directly with high stats and caster level, and stat increases being automatic, and saving throws in general being weakened for martials to fit aesthetic looking charts - meant that spells relying on a single saving throw became incredibly overpowered and things like Magic Resistance (now called Spell Resistance) became trivialized.
Add to that the high 'wealth to level' amounts, and the straightforward magic item crafting rules, and the new '+1 to +5 to ability score' classes of magic items, and the rules gave the Wizard player fiat to craft monsters.
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So, how to break a game as a Wizard:
Focus enough on raising spell saving throw DCs, via stat bonuses, feats, and crafting (which is easy and assumed in the world) and then get a small number of 'Save or Die/Suck/Incapacitated' spells, and no opponents can stand against you.
Multi-class into a few different Full Caster prestige classes that all have a front-loaded benefit, that when stacked together, make for a character functioning 2-3 levels higher than before in one narrow area - say, those high spell DCs - that work well enough that you don't have to become a generalist.
Stack a few buffs and a good Contingency, and you have strong enough defenses that you're impossible to take out before leaving again.
Supplement this with effective 'Scry and Die' tactics, with teleport, so the Wizard chooses the time and place of the confrontation, then leaves when they want to.
Add your usual Nondetection / Leomund's Tiny Hut / etc. and the Wizard is unreachable until a time of their choosing.
Buff out their tower with Explosive Runes and other defenses and attacking them in their home is incredibly costly to suicidal - and that's assuming the foes even have the resources or powers to find them.
So, unless the DM starts equipping enemies with Wizards of the same power level, a Wizard character in 3.X basically 'owned' the narrative. They decided what to do, the spell gave it to them, and they engaged when they wanted to.
We saw it in our games when a total munchkin came in to our group for a 12th level game. He made the Fighter and Rogue obsolete.
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4E fixed it, with changes that worked wonderfully but changed the game too much for a big enough (and loud enough) portion of the user base.
5E tried to fix it in different ways that kept the old flavor, and largely succeeds, but still needs a meta game '6-8 encounters per day' to work or else casters run away with it again. It still breaks at high levels, just like AD&D always did, but it breaks late enough that most players never get the worst of it.
