KOLKATA, India — India is embarking on an expensive last-ditch attempt to restore the heavily polluted Ganges River basin, home to 400 million people. The cleanup will take decades and cost tens of billions of dollars. The World Bank, which has already ponied up $1 billion in loans and grants, classifies it as “high” risk.

Despite the risk — the dangers posed by corruption, incompetence and political parochialism — the National Ganges River ...