I think it's hotstar is just being promoted as the main source of watching these shows that's why they took them off YouTube. There's a whole bunch of popular shows that have been on YouTube for AGES that have ALL been removed now :(
Hotstar's website has a security which prevents people from downloading the videos, whereas it was really easy for people to download them off Youtube. So my feeling is that they've shifted all the videos to hotstar for privacy reasons and to ensure that people can't copy/download them.
Again, this is just thinking, so I don't know the real reason.