tl;dr version: Shoving is a problem, this solution isn’t ideal but at least something is being done.
Personally I have noticed a tendency for the higher level drivers to be far more aggressive with bumping and shoving in corners. I also have a fair bit of experience in turn marshalling for sports cars and know how hard it can be to determine who hit who and how best to penalise them. Down here at the club level in BC we’re lucky just to get enough people to wave flags, forget about rule enforcement.
While I like the fact that the pushing and shoving issues have been noticed and the CIK-FIA is making a move to limit it, I too think the new front fairing system is open to exploitation. Having said that I think after a few pileups forcing half the field to come in for a reset the drivers will learn to be a little more careful in the first couple corners, and repeated complaints of brake-checking would lead to the offender being watched more closely. Unless of course the driver being “brake-checked” is actually ramming the driver in front.
The ideal solution is better enforcement. However, brake-checking with the new system should be pretty obvious to an observer who knows the track and the offender can be penalised accordingly. Incidental contact is something the drivers will have to sort out between themselves, or perhaps learn more to keep their head up to predict whether the driver in front is going to need to slow down for some reason.
Edit: I suppose I should address David’s original question. Should the rear bumper be removed? It would have to be removed from every level of the sport, otherwise drivers moving up to the top level would have no idea how to race without it. I would say no, keep it. Majour collisions and up-and-overs may be rare but they have the potential to be very damaging to driver and kart.