Remember how they're trying to get the demons to live with the humans? I think what's going on is Heaven doesn't want doomguy to kill the demons because it's either:
1) The demons have expressed that they're sorry for what they've done and just wanna live among humans. This is obviously false, but Heaven doesn't realize this (deceitful nature of demons) and thinks they can give penance.
2) Heaven knows the demons will try to kill humanity but wants humanity to learn their lesson, eliminate all demons, and never mess with hell again
3) False heaven made by the demons. I don't think it's made by Hayden as someone said, because he seems like he just wants to leave hell alone and I don't think he'd stand for what's going on in Eternal.
I can't quite wrap my head around 2, as if Heaven wanted humanity to eliminate all the demons, you'd think they d want Doomguy to help, so that's out. I think maybe it's 3 or 1.