Design a replaceable sticker that is applied before every race. The sticker is textured such that it will leave a residue on the offending driver’s bumper when hit hard enough. After the race you can view the front or rear of the bumpers to see who has been rubbing and penalize accordingly. This way we can keep the bumpers and the safety they “may” provide, while also being able to officially call out repeat offenders.
What this doesn’t fix is people brake-checking or using other nefarious maneuvers, however it can show who is constantly causing trouble and allow officials to more closely monitor them (you can be called out more easily if you constantly have someone else’s sticker on your bumper). The material can also be trademarked and coded so that nobody can alter or replicate the material easily. If you never get hit or never hit anyone else, you will never have to replace your material unless you win and are checked for legality.
As a side note, I must be the only one that likes the current plastic bodywork. It gives the kart a level of safety (even if that safety may be exploited from time-to-time), while also keeping the karts from looking like something out of Mad Max. As long as the plastics don’t get overly obnoxious I think they give a certain level of style to the karts, while also giving us enough space for unique graphic patterns.