So if you defined Be = CIR/8 instead of CIR/32, this means that Be is now 4x larger. This means that you are allowed to store up more “credit” of unused traffic so you can burst more later. Keep in mind, that the average traffic rate, over a large period of time, will still be a maximum of the CIR rate, it is just now with a higher Be, you could potentially send 4x as much traffic in a short interval, if you had not been sending the full amount of traffic for previous intervals (hence you have “built up the credit”).
From a provider’s point of view, this could result in a lot more “spikey” traffic (periods of small activity followed by a period of large activity). Most providers would prefer to have a more predicable traffic flow which is why, when Be is even an option with a Single Rate policer, it will almost always be set such the Be = Bc.