If the British monarchy was put to pasture due to Andrew Mountbatten-Windsor's despicable actions do you think coins with the monarchy on them will go up in value even the more recent ones?
Well, if you think of all the combined billions of coins issued under the monarchy, it would take a tremendous upward shift in demand to budge the prices. Likewise, older coins are already valuable due to scarcity or underlying medal value. If there were a "last issued coin under the monarchy," that might attract some interest, but it would have to be a low mintage type to have much appreciation potential.
If my memory of history is accurate, the British monarchy is full of "despicable actions." The problem is that most leaders end up in that category. "Power corrupts" is all too true (if they weren't corrupt already). Based on my (scriptural) worldview, only when a leader loves God and his neighbor, embracing servant leadership while not aspiring for greatness, can a leader truly do well.
True on the monarchy having a history of despicable actions from wars to colonialism to Lord Mountbatten (Prince Philip's uncle, cousin of Queen Elizabeth II) being the OG Amdrew but support for the monarchy is at an all time low IIRC Jamaica even pulled out of the commonwealth so I can see the monarchy dissolving in my lifetime. And you are correct on your worldview.
I doubt it. As others have pointed out, there are just too many of them. Also, to dissolve a thousand-year-old defining cultural tradition on the basis of one man's reprehensible actions would be reprehensible in itself, tantamount to an act of national suicide IMO.