Why are Category II ILS approaches prohibited in an E-Jet with inoperative pitch trim?
Looking at the report, the airplane does not appear to be certified for CatIII in the first place (it would have to have Head Up Guidance and not that many do - the CRJs are the same) so the QRH doesn't need to mention an approach category that the airplane can't do anyway.

As far as CatII goes, the approach with no pitch trim is going to have to be flown by hand, and probably with the existing trim speed different from Vref, unless the trim failure happened while on final while already trimmed to Vref.  So depending on how far away your current, fixed-due-to-failure trim speed is from Vref, you are going to have the hand fly an ILS while holding 5, 10, 15, 20, 30 pounds of force on the column to maintain glide slope at Vref.

This is quite a challenge because the slightest relaxing of concentration will cause you to relax your push/pull a bit and make you drift high or low.  It's enough of an ordeal to do this and stay on glide slope right down to 200 ft.  To hold it down to 100ft, the normal CatII decision height, is pushing it, so the approach is prohibited.