Cruise Climb assumes the ability to maintain optimum altitude at all times which for 99.9% of all commercial operations is not possible due to ATC requirements. In theory the ability to fly along at your optimum altitude for the entire cruise given other parameters equal, e.g. temperature, wind etc , then one would achieve the minimum fuel burn for the same conditions, cost index or Mach number. However, in reality, in most circumstances one can only approximate cruise climb which we call step climb. Be it changing altitude in small increments, e.g. 1000ft or 2000ft at defined intervals will approximate a cruise climb at very little penalty & keep the aircraft in compliance with ATC requirements.
It is possible to cruise climb if an aircraft is given a block altitude clearance however, most airlines to my knowledge do not approve this technique on safety grounds versus little fuel savings.