Pathfinder 1e has mythic tiers that sat alongside class levels that supercharged everyone. Monsters could have mythic tiers too. It sounds a bit like the vibe you’re angling for.
The idea which I don't think you agree with is that high level full casters in 5e (to a lessor extent than in 3e and pf1e though) are already mythical.
The have power, versatility, and reliability that you rarely see in fantasy sources outside supers (Dr. Strange).
IF that is going to remain the case, let's have a martial class that also gets to mythic abilities by high level that doesn't use spellcasting.
Let's also not limit mechanical ways to create these abilities (e.g, fair game to have limited use abilities, narrative control, etc.).
Also if people have no desire for this class to exist or think it already exists or don't understand why it's needed, then just get out of the way and/or support the community members in getting what they want added to D&D as long as it doesn't take away existing options. And as long as said class isn't more powerful or versatile than the current 5e wizard.