They are occasionally, although some sort of screw mount is more common. However it is very common for the tail stock to have a morse taper.
It is my experience to be the opposite.
For me at least, removing the chuck to fit another type of holding fixture is a regular occurrence.
I tend to engrave all sorts of objects in the rotary and a chuck is great for some and inadequate for others.
The best chuck mounting method in my opinion is one that lends itself to easily making up and quickly fitting a variety of work holding fixtures as required.
Greolt