
In your example you used strength and said that a character with more strength will level faster.Yes of course.If he/she is a melee type.Remember that there will also be magic, hopefully some thief type, ranged skill set and maybe others I cant think of now.If made correct you should be able to try all the basic ways to play in the first levels.What kind of game have you running around without any equipment the first levels?Not many.
Besides even if some characters level faster in the beginning doesnt matter much because others will eventually catch up if played correct.
There will always be powerplayers who think being best is everything.I dont think you can get rid of them.I dont like to play that way and Im not alone.Besides their ballpark is PvP and TMW will not be centered around that I think.
If you want to tweak your character while waiting for the next big trait we should use skills.That's what they are for.Having inbetween minor traits seems pointless imho.Also it diminish the fun factor.Traits should be special.

Traits is a base you build on.Your attributes.The basics just like race.Skills on the other hand is something you can train.They should NOT be merged.
Trait -> Strength -> Attribute
Skill -> Training -> Short blades -> Proficiency
You see the difference?
You can combine them for greater effect but merging is going a step to far imho.
Traits are more profound than skills.It defines your character.Adds personality and specialisation.At least in a roleplaying way.
I agree with your last portion of the post.That's what traits are about.Specialisation at the cost of other "areas".