Changing your credit card regularly may "provide better security over time," and it is unlikely to degrade your security significantly. That being said, "over time" is a good way of putting it - you're shifting the odds, nothing more.
It might be appropriate to say: risk = threat x vulnerability. By rotating your card, you may lower some aspects of your vulnerability (but not all). The threat is unaffected. Therefore, you still have risk.
Let me walk you through the thinking that leads me to say this.
Firstly, let's take as a given that card details - number, expiration, name - are enough to allow a card to be used somewhere. 99 out of 100 Internet retailers will require CVV, but that means 1 out of 100 won't. Card Not Present transactions have weaker requirements than Card Present, and when someone steals your card number, they can find a way to take advantage of it, somewhere, somehow.
So that's your threat - if someone gets your card details, and the card is active, they can take advantage of it. Let's talk about your vulnerability.
In some cases, changing your card doesn't lower your vulnerability. Let's say you bought a Snuggi at Target in November 2013; Target was compromised; the card you used is now known to attackers. They turn around and use it. Your annual card cycling doesn't happen until January 2014 - the attackers have a 2 month window to take advantage of your card.
Where your system helps you is when something old gets compromised. Let's say you shopped at Alice's Internet Doodads back in November 2013. AID was compromised in February 2014, and their entire card database got stolen. You, however, are safe - because you changed your card number in January 2014. You have a more limited window of vulnerability based on your card cycling.
(Note that the advent of Account Updater, this may not be true if you previously used the merchant that the attacker tries to use. Maybe someone more familiar with the complexities of Account Updater can weigh in on how a cardholder-initiated account update will get propagated. But it does introduce a case where "old CC# will work".)
I did mention that your system is unlikely to degrade your security significantly - but it can degrade it.. One threat vector for cards is during card issuance - they mail you your new card through the post, and you have to call from the right phone to activate it. But the post is not at all high security, and it's not impossible to spoof the activation call (at the very worst, the attacker steals mail from your mailbox, breaks into your home, activates the card, and steals your Xbox to boot!) Since you're receiving cards more often than average, your risk goes up slightly. It's not huge, but it is a change.