It depends on whether you need someone who can "act like a barbarian", or someone who can, you know, "act".
I don't think he's cornered either market individually – but at least for now, he has a fairly good lock on the "Venn overlap" between the two.
Also, while this may sound borderline racist, there is also a factor in casting roles which gives him an advantage – he is exotic looking, without being seen as too exotic for a mainstream audience to accept… Or put more bluntly, he "passes for white" with the white audiences who care about that sort of thing – which, for really terrible reasons, is still a factor in casting larger Hollywood roles.
We'll have to see how re-watchable Thor is, though. Brian Helmsworth may be able to give Jason a run for his money at some point…