My 2 cents, personally found x/w landings to be a nightmare until I was taught the wing low technique. Later as I gained actual skill my judgement improved and could use either efficiently. Was inclined to teach the crab/kick straight method when instructing.
FFF and Andy_R are correct, the Demonstrated Crosswind is not a limit, but a Demonstrated Component. It would help if people didn't refer to it as a limit- unless it is refered to as a limit by a particular aircraft flight manual.
I also add (from memory) that in Cessna aircraft the Demonstrated Crosswind figure is not found in the limitations section but the Normal Operations section of the Flight Manual (if someone has one handy colud they confirm this?).
I believe also that the Demonstration can be limited by the conditions encountered during the test flight phase- if the cross wind component never exceeded value X then that that is where the notation occured, some aircraft types have had their crosswind component uprated when retested in stronger conditions.