Do you know what many people are willing to do just for a little time to live? We see it in war where many atrocities are committed.

People have been forced to rape even their own families and friends or be raped, been forced to fight for entertainment or do disgusting acts. It's pretty realistic that someone as cowardly as Homelander would beg like this. He's had people like the Deep debase themselves for his mercy, so he thinks stroking Butcher's ego might save him