Of course, we haven't had any instances of jarring physical discontinuities not being accompanied by 'functional discontinuities' (hopefully it's clear what I mean).

But the deeper point is that the whole presumption that we have 'mental continuity' (in a way that transcends functional organization) is an intuition founded on nothing.

(To be fair, even if we accept that these intuitions are indefensible, it's remains to be explained where they come from. I don't think it's all that "bizarre".)