If a region has been home to continuous agrarian culture for many millennia, it will likely be very dense
Which is why Bihar is very dense. So is England
But not US or Canada
Kerala is a bit of an exception here.
But the other regions mentioned were likely "cleared" for agriculture more thoroughly and also earlier than other parts of India
It is a hilly state. So I can't quite fathom what accounts for the very high density. Despite so much of the land being unavailable for agriculture