[Your RPG system sucks!]

Depends on the situation.  For AOE, sure.  For save or dies, yep.  For single target. not even close.  And after spell level 3 or 4, casting times for most spells are so long, those spells only get cast in optimum circumstances.  I wish I had a dollar for every time one of my casters tried to cast a high level spell just to get it ruined.  Example:  Wizard begins to cast Bigby's grasping hand.  Initiative, wizard rolls a 6 (the best possible result), bad guy rolls a 1 (worst possible result).  Wizard adds casting time (7 segments) .  Bad guy adds weapon speed of a +1 dagger (1).  Bad guy goes first, wizard's spell is interrupted.  The wizard has to actually roll a 4 or higher just to get that particular spell off in the same round he started it.  It's so easy to disrupt, it's not even funny.  The wizard can't even use his dex bonus to dodge an attack, that alone will ruin the spell.  This trope of wizards ruling the roost is perpetrated by people who never played the by the rules.

Remember that we're talking about high-level wizards. The fact that they've made it to a high level and survived means that they're probably smarter than any of us. They're very good at taking calculated risks, while simultaneously playing it safe and avoiding stupid mistakes.

 

High-level wizards generaly don't roll for initiative, because it's only necessary in a fair fight. By the time the battle begins, the wizard has probably observed the enemy from a safe distance for a long time. They try to make the initial assault as unfair as possible. There may be traps, summoned monsters, illusions, landslides, and triggered spells all at once. The ambush is definitely not appropriately challenging to the opposing side.

 

As I said, wizards are active characters, while fighters are reactive characters. High-level fighters are good at surviving whatever is thrown at them and affecting their immediate environment. A properly played high-level wizard, on the other hand, takes the initiative and works at a larger scale.

 

In original D&D and AD&D 1st Edition, high-level fighter became lords, while high-level mages became wizards. Both had similar levels of power to affect the wider issues, but while the power of a lord came from their status, the power of a wizard was personal power. While name levels disappeared in the 2nd Edition, game balance remained pretty much the same.

[Your RPG system sucks!]

Really?  A first level fighter with a long sword and an 18 strength in D&D does 1d8+2 damage.  A wizard does 1d4+1 with a magic missile.  At 7th level, the fighter gets an extra attack, for a possible 2d8+2, the wizard can do 4d4+4, about even, but the wizard  can only keep that up a  maximum of 4 times a day.  The fighter can double that output with a decent dex.  You make me laugh.  Until 3e, magic users were NEVER king of the hill.  Sure, they have meteor swarm, but it took 2 rounds to cast and a three year old with a rock could interrupt it.  I've seen that trope, and while it's humorous, it's a spheric cow.  In a vacuum, wizard are very powerful, but in reality most of their spells take too long to cast to be that useful in combat.   3e did away with casting times and 4e just turned every one into a magic user.

Before 3E and other "modern" editions of D&D, wizards were definitely more powerful than fighters at high levels.

 

My experiences are mostly from AD&D 2nd Edition. At low levels (roughly 1-5), wizards needed fighters to keep them alive. While they knew a trick or two, low-level wizards didn't really get anything done in a fight. The game was most balanced with mid-level (level 5-10) characters, when the classes complemented each other quite nicely. Fighters held the line and enganged enemies that dealt heavy damage, while wizards controlled the battlefield, wiped out masses of low-level enemies, and dealt heavy damage themselves. Things changed beyond level 10. While fighters didn't really grow any more powerful, wizards could cast more spells and got access to even more powerful ones.

 

3E changed the balance in two ways. First, the introduction of feats, prestige classes, and other special effects meant that high-level fighters continued gaining new abilities and dealt more damage. Second, the proliferation of magic items added even more abilities to non-spellcasters.

 

To some degree, this all depended on the playstyle of the group. While fighters were reactive characters, wizards were active characters. If the group regularly ended up in an ambush at close quarters, fighters were the ones who would get them out of trouble. On the other hand, if the group preferred to ambush their enemies and fought over long distances, wizards were the ones who did the real fighting. To put it another way, while a high-level fighter could arguably beat a high-level wizard in a fair fight, the wizards who had a habit of ending up in a fair fight with fighters already died at low levels.