My main problem with that is that it feels so forced--and seldom works all that well, either. "Zero level" was really intended to be "brief introductory roleplaying before you become heroes." When people try to use it for "early adventuring as the characters gradually become heroes" it doesn't work nearly as well.
I'd rather there be built into the default enough option, powers, "starting bonus hit points", etc. that you can start at 1st level and not worry about cats or single kobolds. But not have this baked too tightly into the game math. That way, the gradual hero bit can be handled by -- "you don't get all those options".
A similar tweak can be used on the epic end. If you want to continue with that default, relatively smooth power curve, you can. If you want to really rachet it up at some particular point, the characters start getting "epic" options. That way, the sweet spot can be from 1st to max level, but if you want to make a much more pronounced power curve--and manage the resulting issues yourself, you can do that, too.
Maybe, but again you start to run into the "what does a hit point mean" problem. If one group is starting with 10-20 less hit points than others then all the other elements of the game start to lose their meaning because whoever designs a power say that just causes some 'minor damage' can no longer know what minor damage IS. Of course if it is not too far off and the difference tends to become insignificant with time then you could pull it off. Low level stuff might work strangely with such an option though.
I'd think it is best to use 'truth in advertising' in a sense and just make a level below the default starting level for it. There have been MANY different 'level 0' rules out there over the years that produce slightly different feels. Level one OD&D characters would be quite easy to slot in that way, they could just get half the normal hit points and each have one really basic feature of their class like armor proficiency, one spell, etc. Honestly in a sense I think it is likely to be more palatable to most players too. Starting out weaker at level 1 and staying weaker? Eh... Do a level of being weaker and then you're on track with everyone else at your level, cleaner.
As for epic? Just put most of the oomph there into EDs and make them optional. You want a more gritty earthbound high level? Don't use them. Want fantastical stuff? Use them. Each class could get an alternate set of 'no ED' stuff for high levels, so they can still progress.