I think the idea of a roguelike (or a game in any genre, for that matter) where there's a pantheon of gods watching and reacting to your every action Xom-style is really cool. I've seen games where you have different piety or favor or whatever for different gods instead of just picking one to worship like in DCSS, but nothing with quite the depth you seem to be suggesting.
However, I don't think making DCSS that game is a good idea. While DCSS does have a neat Pantheon of gods that get involved already, I agree with Veras' comment. Gods occasionally coming down and doing things, or your actions getting reactions from gods you're not even worshipping, would almost certainly end up somewhere on the spectrum from "spoilery" to "immensely frustrating" most of the time. It's an incredibly neat idea flavorwise, and a cool concept gameplay-wise, but I don't think it fits into DCSS right now. Xom is the only god that acts like Xom for a good reason.
tach3 wrote: (there are already some "god interactions" in game. For example: When leaning axe skill, there is often an an extremely good blade on the 4th dungeon level (that "dev action" could be marked as a "god action")
What exactly do you mean by "dev action" here? That's not a "dev action," that's a random action (unless you're implying that there's actually code in the game that deliberately gives people training axes a good blade on D4, in which case I'm 99% certain that you're incorrect). The idea of random events like finding good items being attributed to gods instead of just RNG is neat, but it might be confusing and lead some people to assume that their actions somehow got a reaction from a god, rather than Trog deciding to drop a random Demon Blade on D4 by pure chance.