Historical Context Is Important
I think that another major reason why the 3.x epic levels (and the 2e "High Level Campaigns") didn't work very well comes down to how the spellcasting classes were presented in the Player's Handbook.
Epic levels had to be "more epic" than casting Time Stop, Shapechange, Gate, True Resurrection, Miracle, and Wish.
This ultimately comes down to planning for epic levels from the start. 8th and 9th level spells -- and possibly 7th level spells too -- should absolutely be reserved for epic-level characters. Trying to add more powerful abilities on top of such reality-altering magic is just asking for trouble.
In retrospect, there seem to be a number of areas where 3e inherited rules from prior editions but completely jettisoned the historical context of those rules. In OD&D, spells only went to 6th level; 7th to 9th level spells were introduced in the Greyhawk supplement, apparently intended for use primarily by the DM in creating high-level opponents.
B/X D&D (and the Mentzer Basic & Expert sets) topped out at 6th level spells as well.
AD&D incorporated the entire range of spell levels, but the general assumption was that adventurers would retire by around 10th to 12th level; Magic-Users received 9th level spells at 18th level, far beyond the expected range of play. The designers of 3e decided that the average group should be able to progress from 1st through 20th level within a year or two of regular play, so now it was expected that most groups would be using these spells.
The D&D Master Set even restricts the Wish spell to Magic-Users of 36th level with a Wisdom of at least 18. 9th level spells begin to be acquired at 21st level, but the Companion Set only contains four such spells (Gate, Meteor Swarm, Maze, Power Work Kill), the rest being left for the Master Set (levels 26-36).
I think that 4e got it right by defining the ultimate limits of PC power right from the start. How do you define spells more epic than Wish? And how do you make any other class competitive with a character that can do better than Wish?
BECMI did a great job of making each "tier" of play feel different by changing the goals and focus of the game, and that's something that should be maintained at least in spirit.
Design the framework of the epic "tier" right from the start -- and we already have a good baseline as to what the ultimate limits of power should be. Then put it aside and detail it in its own supplement where it can be given the treatment it deserves.
Those who prefer a little more down-to-earth fantasy game don't even have to know it's there.