Very often the edge has decreasing effectiveness as the stat it relates to reduces. The inability to take an edge is often tied in with where the edge would be of negligible use if you did take it.

For example, spine of the akragaka works off strength. Felar can't take it. But if they could, it probably wouldn't be doing much for them anyway.

Personally, I like that different chars have different edges available to them. I could see giants getting a crushing blow edge while agile races get a counterpunch edge.

Consider all the other skills that hit back when avoiding an attack:
1) riposte, dex based
2) concealed, dex based
3) backfist, dex based.