I remember in Morrowind, you could be an expert at wielding a long blade, but if for some reason you had to use a short blade you wouldn't be able to hit a thing. That was awful.
Ideally, you could have a matrix determining how much using a weapon trains your other skills. My reasoning is that using any weapon will give you a bit of fighting experience that can be put to use to wield any other weapon.
For instance, using a 2h polearm would give much training in 2h polearm (of course), somewhat less in 1h polearm (perhaps 50% of what you got in 2h polearm), a bit in staves (15%), small amounts in swords and blunt weapon skills (5%), and not a significant amount in the rest (1%)