If you think India sees China as an enemy, do you agree China should also see India as an enemy, albeit an unnecessary one?
That depends on what you consider as enemy. I think a not so competent adversary is better description of India. It's a threat that you need to manage, but I also don't see that much threat from India. If America is 100 in terms of threat to China, India might be 10 at best. So, we have to be very careful to think about it this way.
If we think about US, USSR and China back in the 70s, China was probably India in the trilateral relationship and US managed to get India to join its orbit despite huge philosophical differences because both saw USSR as mortal enemies.
Do we want to get into a similar situation with India? I don't. You have to navigate relationship pragmatically with India and US like you would do anyone else. Sometimes you offer carrot and sometimes you offer stick. It's quite clear that people inside India that can think rationally are also able to behave rationally in transactional relationship.