Not dying of old age is longevity.
That's literal immortality.
Not dying at all is immortality.
If gods can kill other gods, no god is immortal by your definition of the word.
In scientific terms, "all cause mortality" includes not just heart attacks and liver failure and so on, but also car accidents, homicide, etc. By the RAW, a high level Monk is immune to the former, but not the latter

… In my view, a god should not die from a car crash

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...you just gave me an idea for a cool Epic spell, thanks...and no its nothing to do with cars.
Maybe the distinction is debatable, but to me longevity and immortality are different concepts.
If gods can kill other gods then your definition of immortality does not exist anywhere.
Yeah, gods having avatars when they show up in the material plane is a well accepted trope… and them going back to their original plane if slain in that form (just like regular outsiders…) is fine.
The part about the Mythic Form being available as a fallback, but being mortal, can be an interesting mechanic I guess. I can totally see that working great in some specific setting where the DM carefully weaves the story around these concepts. With the right narrative it can land well. Though I think it’s slightly on the exotic side, and in some cosmologies it may feel a bit out of place…
In 1st Edition (for example) you could only permanently slay a god on their home plane (where they were more powerful and had double hit points).
I have taken that and put a twist on it, each god gets two 'set's of hit points, their Physical Form and Mythic Form. When and where the god chooses to stand and fight (and potentially die) in Mythic Form is now up to them.
Player Characters also have that flexibility. If their Physical Form is slain do they play it safe and just go back to their Divine Realm
OR do they throw caution to the wind, stay in the fight, put their literal immortality on the line and create legends.
I guess it would depend a lot on the details… how "mortal" is the Mythic Form really? If it’s squishy (by godly standards) that would probably take away a bit of credibility and immersion for me personally. If it’s nearly immortal in Mythic Form then maybe it’s not a big deal, but then IDK if having the mechanic at all is that useful?
Mythic Form is basically the immortal back to full power
plus it gets access to its Mythic Boon - a higher tier of Divine Boon. Some mythic boons are changes in Physical Form (Hephaestus turns his body to Adamantine), others are not, Ra has a Force Field that radiates Anti-Magic that does not affect his spells/magic, Thor's Warrior Madness grants him Action Surge at will (but cannot distinguish friend from foe), etc. The book has 500+ Boons from Tiers 1-11; where Tier 1 = an Epic Boon, Cthulhu might have a Tier 5 boon or two, so the Tier 7+ stuff gets crazy).
Anyhow… it doesn’t really matter. As long as some folks get value out of it, then it’s great to have that content out there and available! It certainly should not be a goal to please me specifically

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Well I guess I am trying to convince you specifically Silam because I see your position as
identical to mine 20 years ago - when I released the Immortals Handbook Epic Bestiary and Ascension books for 3rd Edition which built upon the Epic Level Handbook and had infinite levelling for Epic PCs - which at the time I believed was the holy grail for epic play.
But it was after years of working on those rules that, from a designer standpoint I started to realise it was just needless complexity for its own sake, it did not help facilitate fun, accessibility, nor balanced Epic/Immortal play - the complexity worked in opposition to those things.
My new approach with 5e Immortals rules is cleaner, simpler, far more accessible, super easy to balance. Yet still has a TON of options:
30 Divine Rank Templates - ie. Immortal 'Levels'
37 Immortal Purviews - ie. Immortal Classes (God of War, God of Time, God of Beer etc.)
500+ Boons - ie. Immortal Class Features.
BUT the simplicity comes in limiting the number of Boons a given immortal can take to very few, most gods will only have 1, 2 or 3. You don't get one every rank
but you can swap all boons each time you gain a new Rank: access more powerful boons, try new builds etc. That's where the flexibility lies.
If you go through the original AD&D Deities & Demigods, immortals had very few unique powers but each power was typically significant, rarely trivial. War gods might never miss, Gods of Magic might cast multiple spells each turn, etc.
Anyway, I'll stop trying to convince you buddy, thanks for your time.