With word processors, etc. it is less literal than figurative. When you wrote out letters longhand and quills, paper, ink were expensive to obtain you wouldn’t throw out the letter just because you came up with an additional thought on the matter. You wrote “p.s.” to add the thought which occurred to you.

Nowadays it is more of a “by the way, I just thought of this” as a polite way to add something, or draw attention to something that might be overlooked in the body of a letter. We know that readers sometimes get a bit glazed as they skim through a letter and the p.s. will receive more than it’s share of attention from a reader.