The dollar-burning mechanism is totally independent of whether or not there are a fixed number of coins. I could see three potential implementations of a CannibalCoin-style cryptocurrency:

(1) Inflationary version: Allow an infinite number of CannibalCoins to be minted, as long as each new one is purchased for a fixed-percentage of a USD. This would stabilize prices near the dollar. It wouldn't make the coin a good source of storing value, but it could make it a more practical medium of exchange by reducing price volatility.

(2) Deflationary version: You mint a finite number of CannibalCoins, but allow people to acquire those finite coins by destroying a dollar. This is actually a method of locking in the intrinsic value of the dollar against future inflation by the Fed.

(3) Upgrading BTC: If there are features that people want out of BTC but are not getting, such as a different proof-of-work method or the incorporation of proof-of-stake algorithms, a CannibalCoin could be set up that would only be sent to people who took their existing BTC and publicly destroyed them by sending them to this address, which is the public-key hash of zero: 1111111111111111111114oLvT2  Nobody has the private key, so those BTC are destroyed forever, allowing CannibalCoin to adopt new cryptocurrency features without inflating the overall cryptocurrency market.