"Several medical ethicists said it would be impossible to get approval for a clinical trial to send a group of children to Delhi to monitor their health."
So what about sending children from Delhi into another places and then comparing them with children that stay in Delhi?
Thousands of kids are already sent from one place to another in India. It's usually kids from cities who are sent off to boarding schools in more isolated locations, usually because the parents have jobs that make it inconvenient to raise kids at home, and often because some of these boarding schools offer excellent education. If they wanted to conduct such a study, they could study these kids.
Or performing tests with livestock (eg pigs), whose lung function could probably be measured non-invasively, and who could be ethically slaughtered and autopsied whereas people obviously couldn't. Animals aren't the same as humans but when the problem is particulate matter and broad-spectrum toxins as described in this article I rather doubt the biological differences would invalidate the observations the way it might if you were studying digestion.
So what about sending children from Delhi into another places and then comparing them with children that stay in Delhi?