Can anyone explain what kind of applications would use or benefit from this type of reduction system? What is the reasoning to go from a belt to a chain and what benefits does it entail?
What specifically are you talking about? Are you saying a motor drives a belt which in turn drives a sprocket that has a chain on it? I've seen that arrangement. Are you asking why a belt was used for the first stage and why a chain for the second?
Belts are generally preferable to chains because they are cleaner, but you can't break a belt and you can a chain. So, some situations don't allow belts.
Which you choose depends on the speed of the chain, above a certain number of meters per second chains become very noisey so a belt would be prefereable, this is why they are chosen for the first stage reduction on high rpm rc motors. for example a chain with an half inch pitch is limited to about 3750 rpm on sprocket sizes between 17 and 25 teeth.