Insulating lowered ceiling above shower?

1970s home, the ceiling directly above the shower is lower than the rest of the bathroom ceiling. BPI certified energy auditor observed a big hot spot in that lowered ceiling and recommended filling it in. After getting in the attic I found plastic stapled to the bottom of the trusses, preventing the insulation from going down into the ceiling above the shower.

I'm planning to just remove the plastic and fill the area with cellulose. Before I do this, I just want additional opinions on why/why not to fill it in, and whether cellulose is the right thing to fill it with.