Your point about Hyderabad leaves out one rather important detail: it was an openly-hostile, pro-Pakistani and anti-Indian state smack in the middle of India; that too a large part. From a political and national-security perspective it made absolutely no sense to leave a sovereign, hostil state in the middle of India. Keep in mind the administration was trying to keep the country together and not get it fragmented.
It wasn't as if India suddenly annexed Hyderabad. There were negotiations going on as well as well as diplomatic overtures. Towards the end, everything was made quite clear when the Prime Minister of Hyderabad, Laik Ali, stated "India thinks that if Pakistan attacks her, Hyderabad will stab her in the back. I am not so sure we would not."
Considering the situation, anything other than annexation would have been foolish and would have put India in a far weaker position and could quite possibly have led to further fragmentation as well.
1. Hyderabad (Osmania) wanted to remain an independent state-- India used force to get them to join the Indian Union, because, in part that it was a Hindu-majority region ruled by a Muslim King.
2. Junagadh (Gujarat) wanted to accede to Pakistan, but India interevened again citing it was a Hindu-majority region ruled by a Muslim King.
3. India annexed the Laccadive Islands even though it was a Muslim-majority region.
4. India, inexplicably, chose not to annex the Chittagong Hill Tracts (East Bengal), which were majority Hindu but awarded to East Pakistan.
5. India, pragmatically, refused to accept Kalat's (Balochistan) accession to the Indian Union.
6. India annexed a countless other land-locked princely states too weak to fend off the Indian Army.
See: https://www.quora.com/India-Pakistan-Relations/What-is-the-K...