How do Airbus planes flare in normal operation?
You don't do full stall landings in airliners.  You arrive over the threshold at reference speed (the full flaps approach speed), ease the thrust off (how soon depends on the airplane, but you need to be at idle before touchdown) and start to flare but only enough to reduce the sink rate to close to zero and then you tease the pitch to maintain a gentle sink until you touch.   If you wanted to do a full stall type landing, there is sufficient energy still available at reference speed that you would have to hold it off and float halfway down the runway, and you'd touch down with the stick shaker going.  Not a desirable outcome in a 150,000 lb soda can.  

If you arrived over the threshold too much below reference speed, there is no energy reserve to save yourself if you are sinking too fast and there goes your tires, if you're lucky.

Water landings often don't go so well if the tail is too low (if the tail touches in too nose high an attitude, it tends to bounce upward and drive the nose over and things can go south).  So it's possible the FBW system actually protected them by limiting Sully's ability to pitch up.  They seemed to have touched down at an ideal attitude, getting a nice ski effect from the nacelles without the tail hitting too early.  

In the famous Airbus airshow incident, the airplane descended gently into the trees as it struggled along way on the back side of the power curve (in that regime, the only option is to descend).  Had the crew more pitch up authority available to them, it is possible they would have semi-stalled into the trees at a much higher sink rate. That was Airbus's response to the criticism over the FBW's pitch limiting behaviour.