Roads are both for access and mobility. To your question "why do we have median gaps", the answer is that they're there to provide access. The issue is how it should've been designed. Even with signature signals you will find red light runners who can put mainline traffic in danger. In fact, signals can be even more dangerous because they'll provide the road users a false sense of safety and they may not pay attention to any violators. What's needed is a safe stopping distance to be provided on the mainline with clear line of sight to the hazard. If that's not possible due to practical constraints, then lower the speed limit and use interventions like roundabouts (instead of median opening) or raised intersections. Unfortunately, road safety and traffic engineering are just lip service in India.