Not really, but sort of
In my experience, Epic Spells are eschewed in favor of normal spells not because those spells are difficult to cast but rather because they are difficult to put in items. Epic Level play is an environment I have found generally amiable to levels of optimization other circles frequently scorn, so most Epic level games I have played in have seen unlimited-use command-word wish slotless wondrous items1 used via speech2 (i.e. as a free action off-turn) to replicate lower-level spells. Usually, these items are placed in a very-well-guarded plane of the PCs' creation and accessed via remote messaging devices e.g. command-word-item Sending spells to servitors near the wish device or a relay station. This means that the game functions on free action time with the PC who finished the wish device's turn never technically ending (unless they decide to let it end at some point). Since the rules say:
An epic magic item cannot be created that uses or mimics an epic spell.
You can't normally put an infinite epic spell device into your private demiplane with your wish device.
That said, you can still cast as many epic spells as you want in a round: since you can take as many actions as you want via celerity abuse and epic spells can be cast which require only a standard action, anyone with Epic Spellcasting can use said actions to fuel their spellcasting and, as long as they yet possess sufficient slots, cast an epic spell. The thing is, you have to be an Epic Spellcaster to do that. Usually after giving at-will wish to one's followers, one more-or-less retires from being directly involved in combats, instead preferring to mostly chain-cast spells with the Fortify Seed, and has those followers go about doing the dirty work instead, assuming there is even still dirty work to be had. Those followers basically never have Epic Spellcasting, so they won't be casting any Nuclear Fireballs or whatever.
And, if your Epic Spellcasting character(s) does end up in combat, their opponent is certainly immune to wish and whatever contingent offensive spells the caster had up and is operating on free-action-time as well so the combat has to be resolved before any Epic Spell can finish casting, since free actions can interrupt turns. If the opponent somehow isn't on free action time, that's not a combat, that's a sense motive check to notice the hostile intent of a statue.
In conclusion, then, there's no situation that sees Epic Spells cast during combat because no high-level high-optimization threat is going to wait around for a standard action to finish.
That said, a caster can certainly cast an epic spell like Nuclear Fireball or whatever, and do so as a standard action, just like regular fireball. Consider the following spell:
Seed: Destroy (DC 29)
Seed: Energy (+19 DC)
Seed: Transform (+21 DC)
Casting time: 1 Standard Action (+20 DC)
Range: 18,618 or 30 miles (+26 DC) (It's not clear, at least to the groups I play with, whether the range/area/duration modifications are multiplicative or additive in sequence)
Area: 4,000 mile or 420 ft sphere (+92 DC)
Damage: 100d20 damage, half fire, half untyped (+120 DC)
The land in the area affected burns, emanating fire out to 10 feet for 20 hours, dealing 2d6 fire damage each round to those unprotected. (+0 DC)
All non-magical inanimate material with less than 15 hardness within the area is permanently transformed into sickstone (+0 DC).
Spell Resistance: Yes
Saving Throw: Fortitude for Half
So we've got a spell with a DC of 327 to cast. That's not really that bad-- our INT should be increasing exponentially at all times so the modifier alone should be way higher than that-- but it still doesn't have to be that high, and besides nobody is gonna spend entire days on developing this: Epic Spells are only reasonable if their final DC is 0 so you can cast them on the fly.
To counteract this, as you have correctly guessed, you gotta use those Additional Participants to reduce the DC to develop or cast the spell. You could instead use Backlash, but that requires a lot of HD and there's no real reason to.
The key thing to note is that the additional participants can participate across any distance. They don't have to be within any distance of you or even on the same plane; they instead just have to do the right stuff at the right time. This means that a tiny subset of your horde of followers (via Epic Leadership or Legendary Commander or both or the Life seed or normal spells via your wish device or similar) can just all take a free action out of turn to cast wish to cast celerity to give up a spell slot gained via Rary's Mnemonic Enhancer to help you cast your spell with a DC 0 Spellcraft check.
- e.g. the following stats from a game from about a decade ago:
Wish on command: [9*17*1800+[(5000*5 (base XP) +5000*5 (so we can make items costing up to 125K gp ) + 25000 (so we can ignore material components on pretty much anything)]*100]*2
Total: 7637700 to craft, ETA 3 minutes after the Flowing Time plane is erected. Command word is 'the'.
- This rule-- that words spoken in speech might inadvertently or deliberately activate items if the command words are 'easy'-- is a rule that is pretty much only sees play, at least in my experience, alongside the epic rules. That is, most of the time 3.5 games steer well away from both the train wreck that is the epic rules and the train wreck that is free-action off-turn custom magic items. However, when a group employs one of these ill-conceived rules, in my experience, they usually also employ the other. My experience in epic games that don't have free-action casting, thusly, has been limited to two games, one of which lasted around 10 hours and the other never really got off the ground. In both the games instead revolved around maximizing one's charisma score so as to best benefit from Epic Leadership in conjunction with Legendary Commander. Combat only occurred in the first one, which was PvP, and as soon as we realized the full scope of the mathematics involved the conflict we switched to using averages instead of rolling and just talked out how the conflict would probably go. We never continued the game from there. This highlights one of the main issues with Epic games: it's very easy to get in a situation where the best solution is just to drop the campaign rather than running every turn in a 10,000 v 10,000 level 1 character fight with scores of higher-level characters dotting the landscape.
Because of this, most successful Epic campaigns I've been in, like most successful normal campaigns, avoid any on-screen conflict with more than a dozen characters on each side. For Epic characters, this means usually any conflicts need to be resolved via proxy and most activity is performed on the world stage via non-violent action.
If you are in a game with Epic Spellcasting but not free action casting and not Leadership and not Simulacra then you are in a place I've not much experience in, and your casting situation will be different than mine. Consider skipping to the second half of this answer.