Hiya!
I don't mind gods being able to be killed by other gods, so even in 5e I'd allow greater gods to be killed by another greater god. As for mortals killing gods, it should be impossible without some sort of divine aid, either from another god, some power equal in power to a god, an artifact/relic, or a prophecy. I'm sure there are other reasons I would accept if I thought a bit more about it. My point is that gods are not the next encounter to be killed by a band of PCs that wander upon it. Allowing PCs to just go god hunting reduces them from gods, to just another Monster Manual type creature.
I don't see any difference between "You can't kill a god" and "Nobody goes god hunting because, well, you'll die". Functionally equivalent. If your players dream of going "god hunting" when they get to high level, the problem isn't with gods being killable...it's that your players are contemplating the attempt in the first place. In other words, the PC's are OP'ed.
We never had a problem with gods being killable (I know, anecdotal, but isn't just about everything when discussing RPG experiences?). I have under my belt three DM's that I have successfully de-programmed (?) from thinking that gods are "easy to kill...because their stats are right there in the DDG". I asked simple questions of them, and they generally answered as I expected them to...ignorantly. So I said I'd run a 'fight' between a god and the DM + Players PC's only using the rules. I'd also point out that the PC's were very much 'Monty Haul Campaign' type characters. As in level 25, or 35, with gold dragons for steeds, multiple artifacts hanging on their belts, etc. Back in 'the day' (1e), it was pretty obvious as to who was running or playing in a Monty Haul game...ridiculous numbers on the sheets, but with virtually zero actual
Player skill. Anyway, for the battles, the god won in each instance. At the end of the battle (which was fairly short on all three, really). They all, DM and Players, said they never knew how tough a god could be. The DM's (and Players) were all using the 'stat block' as pretty much it. They weren't using all the other things a god gets based on it's rank (Demi, Lesser, Greater).
My point is that it is, and should (imho), be possible to kill a god in a "D&D" game. The likelihood should be
extremely low...like single digit percentage if that. Gods have so much to draw on, and so much raw power to command that a group or mortals had better be thinking of the encounter not as "We're gonna kill a god! We'll be legends!", and more of a "We get to be killed by a god! We'll be legends!". Both lofty goals, but the later is much more likely.
That said, I think in some other non-D&D Fantasy games gods should be pretty much "just a name", with no possibility of being slain by a mortal, even a group, hell, even an army (Warhammer Fantasy comes to mind of a game where it is 'impossible' for mortals to kill gods, imho). Most campaigns go by the "gods can't be killed" mantra. But for a D&D game...I have no problem with gods being 'killable'. Then again, with regards to 5e, nobody in my campaign has gotten a character past 7th level, so all the gods can rest easy I guess.
^_^
Paul L. Ming