The Angel pedia entry is a quote from the Masnavi, a series of Persian poetry about the search for God.
Angels and Demons are immortal, be they true or lesser forms. They are reborn in their gods vault, which could mean different things depending on the god. I never allowed them to return to Erebus, deciding that the rebirth and recovery process would take a while (years in some cases). But that was mostly for practical concerns, it made little sence to fight and kill enemies if they would just return in a few seconds to fight again.
Most demons were after short term concerns, so killing an angel gave them what they wanted for a while. And since the compact controls how much influence a god can have getting a significant angel into Erebus was a big deal, losing him was a big loss. Basium however doesn't simply kill the demons he defeats, but has been gathering their souls like a divine jailor waiting for the judge.