Many woodturning accessories (centers, arbors, etc.) have Morse tapers
with solid shafts and no tangs. Recently, in a junior moment, I put
such a center into a MT2 to MT2 extender. The extender has a tang slot,
but the center's taper did not reach it.
I really leaned on the handwheel to secure a heavy blank. Now I own a
dedicated extender with a built in Nova spur center.
So far heat, cold, WD40, pounding, hammer drill, cursing and sweet talk
haven't prevailed against that reluctant taper. I tried a short pin thru
the slot and into the hole to reach the center's tip so as to use a
drift. To get thru the slot the pin had to be so much smaller than the
hole that the drift canted the pin and it wouldn't budge the center.
Moral: when you insert a taper, be sure you have a way of removing it!

What if you put it in a pot of water and put the whole thing in the
freezer. It's possible that as the water freezes, the expanding ice
will force the taper out.

Rust is an issue, but my guess is that the couple of hours it takes
for the water to freeze should be quick enough for this not to be a
problem.