I don't think that there is a loop to close. As long as you pay your annual fee, I think the Bank is fine with you opening up Credit Cards.

I don't think Alaska Airlines minds who purchases the bonus miles to put into your account.

I suppose if you were trying to open up 2-3 accounts at a time and then close them, redeem miles, and then do it all over again, it could/would cause your account to be locked down.

From a Credit Standpoint, I would assume that the bank is only going to allow you to open "x" amount of cards. I would also assume that this type of activity would be on a credit report for "x" amount of years.

I would think that as long as "you know" that you are aren't being fraudulent then this would not be a problem whatsoever.