Nose heavy does more than just create pitch sensitivity with speed. It also makes for a plane that has to land hot in order to keep from bouncing down the runway. It's the #1 setup problem I see with student pilots. Half the time, I can't even make a smooth landing with their planes after they've gotten on the internet and read the advice to go nose heavy for stability. A proper CG will result in a stall that mushes down slightly but still retains some elevator authority, which makes for nice slow and smooth landings.
I'll disagree with the recommendation to go with bigger props too. Trainers aren't slow flyers, and they aren't particularly draggy either. A 12x4 makes sense on a .40 size Cub, but it leaves very little room for speed on a trainer. On windier days, speed is your security. There are few things more frustrating to a beginner than fighting every little wind gust in a plane that won't go fast enough to handle it. The mind gets dialed in to the speed the plane goes, so there is no need to keep it low for students. An 11x5 is a good trainer prop on a ball bearing .46 engine, or a 10x5 or 10x6 on a true .40 or a bushing engine in that size.