So if I understand this correctly, basically you are suggesting that miners mine for short period of time in order to gain proof that they have one work, which increases their voting power? So it is still just as competitive to win the right to sign, it's just that you can turn off the power every once in a while and coast using just your votes?
Personally, I prefer Burst's method. Do the POWs once, save them to a hard drive, then pull them off in real time and present them as proof that you are holding on to a certain amount of hard drive space used to store these proofs. Seems sort of similar in a sense.
If you're worried about power, it turns out that it only uses ~25% more power than POS but is much more secure due to Proof of Stake issues.
And best part, it's already up and running now!
Actually the distribution of voting power does not have to use mining at all. Mining is just one way of doing it - all the voting power can be mined at the beginning until it is all gone. Miners with more CPU power will get a greater number of shares. No more voting power will be added after that. New comers will buy voting power at open market. A better way is to distribute the voting power like shares of a company. Instead of getting more shares with more CPU power, people need to pay more to get more shares. No waste of resources this way. The voting power can be distributed in many other ways as well. For example, anyone with a verified SSN can get 1 share free. As long as the total shares are tracked and nobody can get a controlling stake. In this respect, POR is no different from POS.
What is different is that the method of representation in POR solves the issues of POS like the "nothing at stake" multiple voting problem and long range attacks.
If I understand BurstCoin correctly, its plot need to be mined like POW before it is saved to a disk. This takes time and CPU to prevent it from being created on the fly. There is some waste here but the real waste is the disk space. If BurstCoin ever gets as valuable as Bitcoin, the resource waste will be as massive as Bitcoin because people will invest in more disk spaces as long as the ROI is positive. It is no different than other solutions that require real valuable physical resources like RAM. In POR security has nothing to do with anything physical. It is just a algorithm.