certain motors that are designed differently purely for reasons that the engineer/s thought was best at the time. There are pros and cons for both so there is always a toss up when it comes to motor design.
belt
Pros: quieter, smoother, increased emissions, cheaper, more forgiving of internal engine design. which is why subaru uses them often due to unique engine design.
cons: not very robust, replace more often just due to regular wear and tear, have been used to cut costs, known to fail prematurely for reasons other than wear
Chain
pros: more robust, will last the lifetime of the vehicle
cons: more expensive to replace, stretch over time which results in slightly decreased performance.
For me there is no doubt a chain is better and timing belts have been known to have to be replaced in as few as 60k miles where chains easily go 100k+ The only subaru i know that runs a chain is the new FA20 in the brz and new forester XT. I dont think any STI has a chain and if you ever observed the setup it has ENORMOUS guides to take all the slop out of the chain and can be quite pricey to replace that is usually done with a chain replacement.
A conversion is possible if you are willing to pay the price im sure but it is not feasible by any means.