When to strip vs painting over existing paint?

I need to repaint all of my door jambs to match the new trim that i've put in. The house is old and the jambs have 40+ years worth of paint on them, who knows how many times they've been painted over.

That said, they are in good shape and none of the existing paint is peeling, chipping, est... Despite that, my dad seems to think that the best course of action is either to strip the jambs with a heat gun or replace the jambs all together before painting. His rational is "who knows how long that old paint is going to hold up?"

With a new baby in the house, time is my biggest restraint so i'm much more inclined to just give them a quick sand and hit them with a coat or two of fresh primer then paint. I just dont know if it's worth the time / effort to remove the old paint or rip out / install new jambs.

That said, what do you guys look for when you're deciding to either strip, or paint over an existing finish? Do you care how old or how many layers of paint are already in place?

Thanks