You're looking for a feeling of completion. This doesn't seem to have to do with actual competitiveness.

If you are saying that those lists are required to be competitive, I disagree. Thanks for showing me some examples of what you are thinking though so I can see where you stand. Let's look at the warrior list:

Seven winds: Slight advantage
Seasoned traveler: Convenience (Healers)
Healing edges: Convenience (Healers)
Swiftstrike edges: Slight-medium advantage
Wise recovery: Convenience
Speed flurry: I wouldn't even take this unless on an arial, but I haven't done elf so I may be wrong on its efficacy
Furious Whirlwind: Sounds like a big one
Gift to the Departed: Slight advantage

So the only edge that one would "require" is likely furious whirlwind and sometimes speed flurry. The rest aren't necessary for competitiveness and/or offer only a slight advantage. I'm pretty sure edges that "make X better" aren't by very much, based on immortal input on how edges work in general and experience.

Fact is, you don't NEED any of these edges (aside from, as mentioned, one or two from your lists) and they only give slight advantages (in most cases) so the system is working as was intended.