Only thing I can imagine is removing material will increase the likelihood of warping, but it's probably negligible. If you do it let us know how it turns out.
I have a few pieces of CI. My go to is my grandmother's 12" skillet. She used it to make homemade quick bread in it (essentially self rising flour and lard). I think she had it for 25-30 years before I got it. For eggs, I use 2 tbsp of olive oil and a little butter. That's all it takes for a good pair of SSU eggs.
Copper has amazing thermal conductivity so it heats quickly and extremely evenly as well as cools quickly. For some things, this is crucial.
This... Trying to make any type of cream based sauce is a thin pot metal sauce pan is a crap shoot at best. Hate it.
Enough on the chemical crap.... On copper, I do need to use my revere ware stuff more, out of practice with it so last few tries haven't been great.
Or doing egg whites. Bling. I have one copper pot I like to braise in (as is common in latin cookery) I picked up for a few escudos in northern Portugal 27 years ago. Still going strong.
I've polished several for myself and others. There is no downside other than the time and mess. Polished cast iron is really nice to live with, in my opinion.
Can you elaborate on this a bit? What tools/techniques were used? How much material did you remove? Any before/after pics? TIA.