My understanding is the waistcoats are worn under double breasted jackets so the braces and most of the shirt are covered when the jackets are removed. One mentioned shirts at some point being considered a form of underwear to be hidden as braces are.Why would you do that?
My guess is someone working at a large desk or drawing board may prefer working without a jacket.
Some show some of the vest above the lapels and some don't.
The vests with double breasted suits goes back aways as shown in these images.
Odd vests would allow these benefits after the suits were acquired without vests. I've read of people wearing odd vests with double breasted suits, but haven't seen any pictures yet.