The actual a/f number is not something magic and may be different for every car to a slight degree...what we want is to run as lean as possible without detonation so the nb works well for that...the wise will add a bit more fuel back in to account for things that might trigger detonation.
At idle, all I want is a smooth idle and I want it to be consistent. I prefer open loop altho it helps more on a car with more cam than stock. Again, I lean it down until it starts to waver when the engine is cold, and add just enuf to smooth it out...when it warms up, it will idle over a wider range without a problem. Both my cars like it somewhat richer than stoch so closed on a nb is not optimal.
I have had good results closed on a wide band...usually around 13.5/1 on a warm engine...but I am perfectly happy open loop all the way