The problem is that they don't pass their digestive invulnerability along with their poop.
It's certainly possible for some other species to have microbial strains that would be healthy for us, and also lack species that would be unhealthy, but the odds are probably pretty low for that happy combination.
I drink rainwater, with only simple filtering, so I'm sure I've consumed bird poop and dead bugs and all their microbes. I don't think it's done me any harm, but no noticeable good either.
I have no plans to experiment with unidentified (or identified for that matter) dung I encounter in the woods.