Not necessarily. It would seem to me that when changing from IAS to Mach in the climb you would typically be below MMO (the maximum operating Mach number) and the cruise Mach number which would itself be equal to or below MMO depending on the FMC cost index.
You're correct - climbing at a constant IAS yields an increasing TAS due to a decreasing air density. It's not so much that you 'have to fly faster' in the sense that there's no extra effort; the aircraft accelerates in relation to the air mass under whilst the drag remains constant.
Last edited by bravobravo74; 13th October 2012 at 07:57.