I have never taken off with the packs on on an Airbus.
Fuel saving's the reason.
Boeing has a slightly different procedure, the APU will be on during an no-engine bleed departure since I taking off unpressurised is a bit more problematic on the 737 (pax comfort during rotation due to the open outflow valve) if I remember correctly.
I do not understand your question about flex. What has flex got to do with it?