I love these sorts of discussions; its nice to consider different perspectives.
For me, this is a complex issue. I try to stay away from buying duplicates outright. If I ever buy the same figure its because I am gifting it to one of my young neices ir nephews usually. I would like to buy some duplicates for custimization but I don't have that kind of extra income.
Otherwise it is for reasons as described above. A) to gain a "show" piece for my collection when I have mine from childhood who were WELL loved (I can't part with those even, I have the Schleich
#13211 missing an ear but I just can't toss her away). B) its a color variant. Here I usually only keep drastic variations but sometimes I catch myself making exceptions for models only slightly different. Or C) if it comes to me as "bycatch" I may hang onto it for a bit... but those either get gifted or customized if they aren't a highly tradable item.
BONUS: Or D) if it represents some sort of mystery... I have a mahi mahi figure x3 now. A silver and yellow version, a rainbow realistic coloring version, and I made an excuse to buy a lot with one with much more vibrant red on it... probably don't NEED it but I WANTED IT for the same compulsive reasons you listed for your cats. It is more or less the same paint scheme as the other, but its juuuuuust different enough....
I haven't had many models break on me yet that I wasn't able to easily to replace.
But I am sure the day is coming that will break my heart and I will have wished I had a double.