In minor cases, I see absolutely nothing wrong with canceling a card after the first year. Unsophisticated credit users can easily get a card and find it's not really that great for them. I only applied for PRG because Amex sent me a nice mailed offer and I thought I might not qualify for the card I really wanted, BCE. I got PRG to build a history with Amex, and I've found enough use to keep it beyond the first year, but I would close it if it no longer made sense and I couldn't "justify" the AF.
Even for sophisticated bonus hunters (or people who just want to feel like high rollers), though, I don't think there's anything very wrong with closing numerous cards to dodge the AFs. The fact is that most issuers don't structure incentives to encourage customers to be loyal over the long run; they structure incentives to encourage jumping around. When issuers make the rules and can easily adjust them, you can't really blame customers for acting in unorthodox ways.
Discover's "double rewards for a year" bonus is a very rational and fair incentive, but is the exception rather than the norm.
Issuers could do the following, but generally
1. Offer reasonable rewards and a reasonable bonus.
2. Keep out the apparent undesirables. Decline people with a history of bonus hunting - either with that same issuer, or people who have a suspicious number of accounts with other issuers closed before the end of the 12th/13th month. A person can't do much bonus hunting/card closing without it becoming obvious on his or her credit report. Some issuers have become more careful about this.
3. Keep nerfing to a minimum.
Instead, issuers usually focus their efforts on opening new accounts, and I expect that nerfing would happen anyway. A card program becomes really
profitable when the only people who still have it are the ones who don't pay close attention to their rewards. People who jump ship after getting a bonus generally only accelerate the inevitable.
If closing a card to avoid an AF is bad, then other activities look questionable...
The vast majority of my spending on Sallie Mae is 5% stuff. In a small way, one could argue, I'm abusing the rewards system and encouraging Barclaycard to nerf it. Barclaycard gets about 2% of the transaction and pays me 5%. I only spend on BCE when I'm using an Amex offer.
I put a lot of 10%+ stuff on Discover. I even heard one Discover shareholder complain about the company's margins getting too small. I was only too happy to explain my contribution to that.
The point being...although my accounts are staying open and don't look suspicious on a credit report, I'm not using most of them as the issuers intend/hope, and I'm doing my little bit to make the rewards programs unsustainable.