This started the train of thought - What is the "proper" way go about
removing something (i.e. the chuck for starters) from a morse taper
interference fit?

As a follow up to my previous post, I remember that the centre on
lathes is usually removed by backing up the tailstock, the tailstock
spindle has a pin which pushes out the centre.

Of course if the taper has been seated for a long time to heat up the
outside with a blowtorch may be useful...