It will have negative consequences as far as incapacitation goes, and high rank areas as a whole. "We don't want you because you cant do this to this monster". Good if you ranked every battle class to 50 and dont give a shit about anyone else.... There are already a few weaponskills that require you be the class.
There are skills however that cross-class very well like Feint as well as skills we need for Incapacitation. If you restricted those it would make things like incapacitation harder, especially with the 8-player group restriction. It wouldn't be extremely helpful if you HAD to bring a certain class along just to incapacitate and then just take up space after that.
I don't see these being incredibly important factors. Most of these are balancing mechanics, and I'm more focussed on the overall game, class uniqueness, and the animations. I know there are some class restricted abilities already. I think Simian Thrash is probably the best example. It's probably the most visually impressive, and this it is because they only had to make one animation and 1 set of effects that matches perfectly.

Perhaps we may end up with a mix of both; weaker less important DPS abilities, but good for incapacitation, available to every class; and then, several class specific abilities that bring uniqueness. Either is an option, and seeing as how restricting the abilities already in the game would then mean they'd have to go back and make new animations... probably highly unlikely.

I suppose instead of asking to restrict all weapon skills, although Xenor has a good point:

They're called weapon skills for a reason. Why should an axe weapon skill be able to be used by a bow?
It may be better, moving foward, if we ask for all new abilities to be class restricted and much more visually impressive.