I find it much less jarring with linear interpolation than cubic, and the overhead of doing a "clever" (ie world aware) cubic interpolation is probably a LOT bigger than you assume. I'd rather list all collisions within a tick and interpolate linearely between those.
Including acceleration in the interpolation, however, is a very good idea if you manage to do it right, but it'll only matter in games where things change direction a lot.
But I guess the only reason to not do it state based to avoid that single frame of latency? Seems pretty negligible, but I guess if you're doing a super-accurate simulation or something it makes sense.