I'm going to go out on a limb and suggest that, for the most part, we are not training the core with a "core" day.
Squats
Deads
Pulls
etc.....WITHOUT A BELT - keeps the core in shape.
I DO think its important, at least for ME, to hit some weighted standing cable crunches and weighted hypers and/or/ seated gms...to ensure that there are no strngth imbalances.