So if a broadcaster shuts down a channel and airs it content in some other channel in wstershed hours then only reason is that its employees/content team like the content .....firstly buddy i don't know whether u wrote this as sarcasm or u were serious about this statement but i can list put numerous examples where other broadcasters too have done the sams.
Real reason is that post midnight many channels air fillers for many hours rather than regular content, same is case with Star Movies.... Now as Koffee With Karan is a higely popular show then maybe they would have decided to ait it at midnight just to see if people watch it before sleeping or not as many people search for such shows to just relax mind and enjoy, also it helps fill the vacant slots in these hours so it is better to air a popular show than some random fillers.
Lastly their team do not require to air a show on TV channel to watch it as theu can easily access it on Disney+Hotstar