The problem is not so much the marginal rate of climb following an engine failure shortly after take off, but the failure of the pilot to take instantaneous corrective action including the feathering procedure. The flying schools teach an often inappropriate lengthy period of identification via various methods, and often critical seconds have gone by the time the pilot gets around to actually feathering the propeller.
A generic drill mouthed by the pilot may include identification of the failed engine by the direction of initial yaw (dead side - dead leg etc). Then a careful check of the engine instruments to confirm the cause of the initial yaw. Then a further confirmation takes place by slowly retarding the throttle of the suspect engine. All this time the colossal drag of the windmilling propeller is taking steady toll of airspeed and within literally seconds the airspeed has dropped 10-15 knots from the initial engine failure figure.
The fact is the feathering of the propeller must take place immediately after the engine failure is detected in order to stop the danger of speed decay. The risk of closing down the wrong engine must be balanced against the certain potentially fatal loss of airspeed that will occur unless the dead engine is feathered without delay. The act of closing the throttle of the suspect engine as a means of confirmation, raises the question of how fast do you close that throttle lever. It is generally accepted as a slow movement just in case the wrong throttle has been closed and you don't want to momentarily lose all power (wrong throttle pulled back and dead engine already dead equals a problem!).
A slow pull back of the suspect engine loses more precious seconds of windmilling drag and thus decaying airspeed. To competently handle an engine failure after take off at low altitude requires instantaneous correct feathering action without the luxury of "dicking around". This way, the danger envelope of windmilling drag is minimised to perhaps around 5-8 seconds. But to arbitarily state the pilot should deliberately close both throttles and crash straight ahead simply because the altitude is less than 500 feet when an engine fails, is shutting off all options that may have been available.