Mythological figures are characters whose stories have long since been written. What they could do is what they were depicted as doing, or on the outside authoritatively described (no 'said to....') as able to do. Nothing more.
Yet other authors have taken these characters and played with them adding powers and capabilities, even D&D designers themselves when they statted out characters like Circe and Hercules. Though they give a few martials caster levels to show their magic.
As has so often been claimed on the other side of this argument, PCs aren't supposed to be actual Gods. (Circe was the daughter of Titans, though, and Titans and Greek gods, both, tended to have powers limited to a portfolio, like Domains).
You just argued for why martials shouldn't have mythic abilities. They are not gods. Characters like Odysseus, Perseus, and Jason exhibited very mundane martial powers because they weren't gods. Casters in stories do not exhibit the same mundane powers.
And, way back in the early days of Dragon Mag, it was pretty convincingly argued that a 5th level magic-user could have done those things. Of course, he had the excuse that he needed to 'hide from Sauron.'
I've heard that. By D&D standards he was probably a 5 or 7th level wizard. A 10th level fighter. A bit of druid, maybe 3rd or 4th. A bit of rogue. And an angelic being. Yet even a 5th or 7th level wizard exhibited far more powerful capabilities than any martial in the story. You just supported my argument. A 5th level wizard still exhibits capabilities no martial can accomplish because the caster-martial disparity has existed in D&D since way back in the day. Even a 5th level caster casting a
fireball was far more powerful than what a martial could accomplish with this weapons.
The caster-martial disparity isn't just a high level reality. It's a reality from level 1 when the caster can cast
charm person and the martial is swinging a weapon. Even at level 1 the wizard has more power to affect the world in a broad way than the martial.
He knew hundreds of passwords used in spells to seal doors.

In D&D terms, he cast Hold Portal.
And he new hundreds of ways to open doors.
knock,
wizard lock, and
hold portal.
Generally not. If a caster ally of the hero was reputed to have great power, like Gandalf, there'd be some plot-point keeping a damper on it. If the Hero himself, is the caster, he's either very limited in what he can do (or what he needs to do it), or the whole work is scaled to that power (like Lensmen throwing planets at eachother).
First part true. Second part usually means the protagonist needs to go through some kind of journey to obtain his full power, once he obtains it he becomes the legendary power he is destined to be.
Level, alone, easily takes care of that range without having to make casters supreme at every level.
At every level a caster is more powerful than a martial in breadth. Even a 3rd or 5th level wizard can do more than a 10th level or higher martial in terms of scope. Damage wise martials have always done more single target damage. That is part of their appeal. I don't care about being top on the DPR meter. I care about effects and other forms of manipulation. Magic manipulating the world in powerful ways is what I look for. Breadth, not necessarily damage, is important to me.
Again, you're mistaking rep for ability. Casters tend to have fearsome reputations, but they also tend to lose every time. In fiction, that's the author's power of plot, but in a game, it has to be reflected in stats. 1e, though it gave PC casters far to great a breadth of power, handled that last bit well at high level: the horrible uber-magical threat would hurls spells at the protective-item-festooned party, who would all save unless they rolled a 1.
They lose because it would be unsatisfying to have them win. It wasn't quite a 1 for all saves, but for quite a few. It depended on the class. 1E casters were still more powerful than martials in nearly every area other than damage. We're not arguing damage here.
A lot of them /need/ to, because their magic isn't effective or can't be brought to bear in actual combat.
Or because magic use usually has some debilitating effect which D&D decided not to incorporate. Gandalf felt drained after using magic. Raistlin the same. Using magic was physically taxing. 1E had a few mechanics of this kind with the system shock roll for spells like
haste. 5E has incorporated some mechanics to simulate this with the Concentration Mechanic and spells like
wish possibly messing you up pretty badly. I'm happy to see these mechanics incorporated. I like flavor mechanics that give casting a cost or limitation. Casting is hard to learn, harder to learn than swinging a sword in fiction. Magic users are usually extremely rare due to the physical, mental, spiritual, and sometimes other costs associated with its use. That part of fiction D&D hasn't captured very well in every edition. Some parts are left up to the DM like the cost of summoning otherworldly creatures.
3E left a bunch of this stuff out and went too far empowering casters. I feel 4E went too far disempowering casters. I think 5E is much closer to my tastes for fictional magic. I love they got rid of memorized slots and went for the general spell list mechanic. 5E's magic system is probably mechanically my favorite of any edition.
They have that rep, they do some large-scale rituals, but they wouldn't be helping the hero if they could do what he could, they'd just wave their hands and solve the problem. They don't, because they can't.
Depends on the book. Sometimes a much weaker wizard travels with a much stronger martial. Sometimes a much stronger wizard travels with and protects a much weaker martial. Sometimes they are relative equals. It varies from book to book. Always the martial brings a caster that can do some extremely powerful things he cannot do.
Once again this isn't argument about damage. It's about breadth of power. Martials in every edition have had immense killing power. 3E martials make 4E martials look like children playing with sticks. Yet this is forgotten in the caster-martial disparity argument. People unhappy with the disparity always bring up all the nasty spell combinations casters did in 3E that made them so strong. Yet they never bring up the 300 plus hit point rounds of damage by martials critting like crazy. Of the 7 or 8 arrow attacks. Or the +40 damage. Or the ability to literally pulverize castles and dungeons with their weapon cutting the places to pieces. Or the fact they could take on a giant army and cut them down. Casters in 3E couldn't afford to get hit by a 3E martial because they would die in one round.
It's been that way in quite a few editions. Casters survive by not letting martials get to them or using magic to mitigate their attacks. That's also part of the fantasy genre. The lessons casters learn is don't let Launcelot or Conan get a hold of you or you're dead meat. That's why casters spend so many resources on ensuring the enemy can't lay their hands on them, while martials wade into battle.
Gandalf desplayed casting ability that a 5th level wizard could duplicate. Merlin didn't do a lot better, depending on the story, maybe he cast a 5th level spell, once.
And you're just further illustrating the caster-martial disparity. A 5th level wizard can accomplish what Merlin and Gandalf can, it is still far more powerful than what any martial in the story did. Launcelot and Arthur were definitely higher than 5th level fighters.
Folks have gotten used to it, after decades, but in the early days of the game, it was a source of a lot of criticism, not just because it was mechanically broken, but because it was nothing like the magic in any fantasy genre source (Vance be sci-fi). It was used /in spite of/ being totally genre-contrary and unrelatable. Because it could be made to work, mechanically.
I do not recall these arguments and yet I was playing during that period. My group and I found the magic to be very relatable to fantasy. You're simply applying your viewpoint as what, the majority viewpoint? The minority viewpoint? I was there when D&D first came out. It was well received including the magic system. If there were some vocal critics of it, and I'm sure there were, they certainly did not stop the game from becoming the most popular in history. D&D doesn't do things perfectly, no game does, but it mirrors general genre conventions well. The only problem many have is it lumps all these genre conventions under one roof. Sometimes that is hard to manage.
You'll never win the caster-martial disparity argument as far as fantasy goes. It is very much there and not just defined by levels. Even low level casters as you have so clearly attempt to illustrate with Merlin and Gandalf are some of the most powerful beings in the entire world exceeding what martials can accomplish. It would follow that even higher level casters would be even more powerful. Authors, and game designers it seems, can't imagine a world where magic is on the same level as martial weapons in areas other than damage. I can't either. Not sure why you can. Magic should be something amazing, far more amazing than picking up a sword and swinging it. I don't see why you think they should be comparable for any other reason than game balance similar to what you see in MMORPG. The main reason it is necessary in an MMORPG is because of PVP. D&D is not a PVP game. It shouldn't be designed as such.