I've always felt a good way to handle skill pools without having everyone being world-class at one thing in every pool is to create an attribute for each skill classification. This attribute influences the size of the skill pool.
For instance, Athleticism for strength/stamina skills, Coordination for more precise physical skills, Arcane/Piety for magic/religion (in games that have those things), Memory for knowledge skills, Artistry for fine art/music/dance skills, Handiness for craft skills, etc.
This way people can be jack-of-all-trades, master-of-none if they choose ... but if they want to be the absolute best fighter, they have to pump their Athleticism and/or Coordination, so that the others are less developed. Meanwhile, a hardcore crafter might focus on Handiness, with Memory a strong second, and maybe a little Artistry - but this leaves them with a rather mediocre Athletics, Coordination or Piety pool.
There's still a fair amount a customization possible. A battlemage (in a game with magic, of course) might spec Arcana and Athleticism, while a traditional mage might be Arcana + Memory. Even a pure fighter can elect to be an exceptionally powerful skullcrushing juggernaut (but only above average in finesse) or an exceptionally well-coordinated swashbuckler with only above average strength -- or something between the two.