But the mechanics of the powers still speak to that type of fantasy... earlier someone quoted something along the lines of "When you die for the first time today..." It's pretty hard to refluff casual self-resurrection as "realistic"... even D&D realistic
Three options off the top of my head:
Don't take an Epic Destiny with a casual self-resurrection option. There are plenty of them and they're often usually better — simply because options that trigger only when you die tend to create reasons why you might die in the first place. Destined Scion is a great ED as an example — if you're unconscious, once a day, you get back up on your turn.
You have a magic item that explains X, but it isn't actually listed on your sheet. You, yourself, can't self-resurrect, but that magic charm you found at 24th level does it. And your DM, because they're interested in a realistic outcome and you described your choices, helps make sure that happens.
Death in D&D is often a Schrödinger's cat problem for realism anyway. 1 hp PCs basically fight as well as they do when at max hp. They just go down much easier. So a realistic explanation for hp is that when someone is dying, we don't know if they're actually dying or not. We just know there's a chance they could die. How do we know if they died normally? They failed a certain number of death saves or dropped to a particular number of hp. But when you're an Epic PC, once per day, those aren't sufficient for certainty.
Honestly this is baffling me we have [MENTION=42582]pemerton[/MENTION] claiming mythical fantasy is an inherent part of 4e but then you're saying it's casually easy to remove it... which one is it?
He's not claiming that? 4e strongly supports a mythical fantasy type of game by offering choices that support that style of play. You don't have to do that unless you want to do that. And again, that's a decision made by the table. Which can mean the DM enforcing a style of play or the table as a whole deciding to do that. But the table knows that at 1st level, not because the player gets surprised at say 7th level that they're not allowed to do cool things because the DM has decided Come And Get It isn't sufficiently realistic.