Rainer
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He recites a prayer and asks them for help before the battle, and that's when they arrive. In reality, they are not always in your army; the icon is just for show, indicating that they exist, and they only appear during the battle. And in the temples built in the cities, people bring them donations and gifts.
Added 2 minutes later
And since this is primarily a strategy game, many nuances can be omitted. Thus, the cost of hiring an archangel is something like a donation.
Added 1 minute later
The hero doesn't need to control them if he is truly a HERO. Remember how the archangels left Isabel.