I don't think changing the boundary to place=city would be correct, since Delhi still have some villages in it. Nor do I think it would be a good idea to have 2 Delhis, since people don't make much of a distinction between the two. (Delhi city encompasses almost all of the area of Delhi state, even villagers call they are in Delhi city.) Are you suggesting changing just the label to place=city? Would it cause any problem with Delhi relation which should contain place=state?

(BTW, I think one can see the word "Delhi" on the map if they zoom out, like other Indian states like "Bihar." It might be hidden because it is very close to "New Delhi", the capital of India.