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Just removed my spare tire keeping the carrier and just ordered a 24" round heavy duty Christmas Wreath storage bag that I plan on using for extra packing space when my wife and I do a 10 day trip this summer. Figure we can carry a couple small bags inside with t-tops and pull out the bag from the spare tire carrier every couple of days to swap out clothes.
If I did have the carrier and was carrying around a flat spare I would get a new tire mounted on the spare hub and keep it there. Simple to change a tire and off you go. To me it would add a bit of security.
I have had a flat tire on my C5 and just plugged and filled it with the pump because the C5 has no spare. But it would have been nicer to just change the tire.