wrote

I'm finishing my basement and I've primed all of my walls. I was
planning on completing the painting of the walls first - then painting
doors and trim and installing them. I thought this would save time as
I don't have to worry so much about masking everything and I can spray
just about everything.

This seems to go against what I've seen done. What is the problem
with my approach?

No problem. It's the fast way and it works fine. You'll have to touch up
the woodwork after installing it, but it will look just fine.