The biggest issue with this idea except for the bandwidth, is that you won't have a good idea of how many computers are generating in the network, or how hard it will be for generating.
This kind of information is useful when buying/selling bitcoins, as it has an effect on the price.
Also, I wouldn't know myself how easy it will be to generate, possibly wasting CPU power and electricity in my computers.
I rather stick with the system in use today.