In the Airbus A320, why do we need to level-off for flap-retraction after a single engine failure?
Even if we maintain a climb, the airspeed will still accelerate and be enough to retract the flaps safely.
In a nutshell: the aircraft has lost 50% of thrust capacity, and you can either choose to make a shallow climb, or accelerate in level flight to retract the flaps. Unless the aircraft is very light, you cannot do both at the same time. The performance is just not good enough.
You might even decide to increase the thrust on the remaining engine to TOGA, because when the aircraft is very heavy, it hardly climbs or accelerates if you keep it at FLEX/MCT.
Additionally, you need to accelerate to certain minimum speeds first (F or S speed), and then retract the flaps step by step, which then reduces drag and makes further acceleration easier.
You state that after a single engine failure, the aircraft would still accelerate while climbing. Where does this experience come from? A professional simulator, or a simple aircraft model in something like the Microsoft Flight Simulator? Could it be that your model is just not accurate enough, or you have made unrealistic settings like payload and fuel which makes the aircraft unusually light?
The climb segments defined in the FARs or European equivalent are used for certification purposes. The different climb segments are designed to allow the engineers the ability to easily calculate performance during a climb.
Many aircraft procedures are designed around these requirements. Airbus aircraft will level off to accelerate to VFTO and bring the flaps up so they know what performance they have. It may be possible to lower the nose a little bit and start accelerating while still climbing but it would be unknown what sort of performance they would have. If there are no obstacles, it may be a good idea to do that. Leveling off, accelerating and bringing up flaps reduces drag and an increased climb rate may get the airplane to 1,500 FT AGl quicker than other procedures.
Other types can make low rate climbs while accelerating on one engine. eg B767 SOP is Vertical Speed +200 at low and medium weights once terrain clearance has been achieved. At heavy weights VS +100 is used. I guess if near MTOW at high density altitudes level flight acceleration may be necessary. Pilot’s judgment was used, not specific weights at my old company.