I carry mine, and when I check in, I present it along with my credit card. I am guessing that it has prevented missed credits, etc., since I have never had the problems that are often described in this forum. Also, when I give the card along with my credit card, the clerk is already thinking 'upgrade' even though he/she should start thinking that once he sees my record.
It's never been received rudely at all, and I believe that the desk clerks are either pleased to have been shown the card or they are neutral (which I suppose is what one would expect).
FWIW I also carry my Adm. Club card since that's always needed and my AA Exec Plat card. I don't carry any of the other award cards unless I know specifically that I am flying on that airline or staying at that hotel chain.
Makes for a slightly thicker wallet, which is the downside.