As a Mumbaikar living in the Netherlands (where OP appears to be), you're right - such underpasses will be a terrible idea in the monsoon season for Mumbai-like

As a Mumbaikar living in the Netherlands (where OP appears to be), you're right - such underpasses will be a terrible idea in the monsoon season for Mumbai-like places. However for the Netherlands, rain is much more evenly distributed across the year and even "heavy" rain days are much lesser than the amount of rain a tropical city like Mumbai gets - which is why it's unlikely to be a major issue in the NL. (Side note I don't think there are pumps at every underpass if at all, perhaps only if the underground drains/sewers overflow. Also NL maintains high sea walls/dykes partly out of necessity so there likely will be place to pump it here.)