As far as I know, the reign of the Mughals was somewhat of a golden era for India, bar Aurangzeb and his successor's failings, so was there any desire to restore the monarchy after the 1857 rebellion, or during the later independence movements?
Well, I'm a month late and just searched around and stumbled into this thread noticing noone responded. I just read the top comment here https://www.reddit.com/r/AskHistorians/comments/3jhdjo/do_the_indians_of_today_still_consider_the/ where it's mentioned that, in the new government of India, the latest Mughal was wanted.