Gday Bojan
Yep. My old drill press has a MT2 spindle, then MT2 to B16 adapter, but on checking, the MT is a blind push fit, ( no drawbar locking it in ).
ie when you fully wind the spindle down, there is a slot in the side of the spindle and this allows you to use a std tapered drift to remove it.
My mill also uses a morse taper spindle, but it is held in place using a drawbar.
One thing to consider re trying to use B16 the way you want
It looks like this is a "quick fit" type connector designed for "drills"
ie where the load is always pushing the chuck onto the spindle and is central to the axle.
Not sure if B16 would be safe for a true lathe chuck that can be loaded in a series of directions
Ever seen a chuck/faceplate spinning across a floor :-)
Andrew