Usually the "complete package" metaphor would be used either to mean either "well rounded" or, more narrowly, "has enough of everything needed to be successful at the highest level."
It would often be used by commentators discussing contenders at the highest level to compare skaters who reached that level purely on extreme technical strength (figures and/or jumps) vs. a skater who was merely good to very good in that technical area and also good to very good in areas where the technically superior rival was distinctly lacking.
For example, consider the following quote from the heyday of the "complete package" discourse:
This was coming from a skater who was known to be flamboyant and to be inconsistent at a jump that defined medal-winning programs at the time."The biggest thing is that I've made people happy by skating," he said. "The biggest thing I've tried to emphasize is the more diverse choreography and artistry through technical ability, so you have a more complete package. I think that's a wonderful thing, and I'm proud of it."
And here's a fan(?) writing 2 years ago that
You can find the term used in several different shadings of meanings, but I can't imagine any shading in which the presence of something (flamboyance) would disqualify one from complete package status. What would disqualify would be incompleteness -- a lack of something -- whether that be edge quality or jumps or "artistry" or head for competition or whatever.Chan, Lysacek, Oda, Takahashi, and Weir have the complete package! It will depend on who will make the least number of errors.