If you’re serious about solving this sort of problem, you’ll need to reverse-engineer the Word XML for this aspect of tables.
The place to start is with before and after (adding a column) XML dumps of the table, identifying the changes made by Word, then duplicating those that matter (things like revision-numbers probably don’t matter).
This process is simplified by having a small example, say a 2 x 2 table to a 2 x 3 table.
You can get the XML for a python-docx XML element using its .xml attribute, like:
print(tab._tbl.xml)
You could compare the deepcopy results and then have concrete differences to start to explain the results not working. I expect you’ll find that table items have unique ids and when you duplicate those, funky things happen.
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