Has knowing those factorisations come in handy?
Not at all. Do you think I would stuff my primitive cerebrum with the mere memorization of identities? But the looking up of them when necessary has been a great help.
In mathematics, you don't understand things. You just get used to them.
I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.