as long as you are within WAT limits and there are no obstacles to consider you are not climb limited
Got to disagree with you, if you cannot achieve the required certification climb gradients you are climb limited, if you cannot clear obstacles in the takeoff flight path then you are obstacle limited.
Regardless of the nomenclature on your takeoff charts, these are the limitations. To test it, pick an airport with no obstacles and a long runway, then increase the airport elevation and temperatures until you start to see restricted takeoff weights less than the structural, what do you call these weights? Mr Boeing calls them CLIMB LIMIT weights.
Mutt