You make (9*5) 45 fire quanta but only use 28.
Rebirths.
You plan to rebirth a phoenix 17 times? In a fast deck?
In a fast deck, you can't really go with 4-4 phoenix-immo, because if you draw them on a less than one-to-one basis then the phoenix would be dead cards.
one cremation + five novas = two phoenix
two cremation + three novas = three phoenix
three cremation + one nova = four phoenix
four cremation = five phoenix
Not to mention how much of a pain devourer, rewind, and fire shield is.