tl;dr - total electric consumption will not be reduced by implementing the OP's proposal.
I'm sure the miners wouldn't be supporting such a thing because it just makes it even harder for them to get a reward.
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Also, if there are millions of miners and you randomly select 100 of them, you encourage the rest of the miners to form mining pools. Then, you will end up in a situation where 100 miners are selected as before, but there are only 100 huge mining pools, they always get everything and distribute that to smaller miners. Almost no solo miner will follow your system if that miner will be rewarded once per month, because the risk of price drop after entering exchange is higher than the potential reward from solo mining.
I wonder if the people that wrote that paper realized that. that's thinking ahead!
the bitcoin mining system is really hard to make changes to without causing things to get "out of whack" This is similar to say that miners will organize themselves in big pools to organize a 51% attack on Bitcoin network. It did not happen so far.
Miners engaging in activity similar to what I described is similar to miners attempting to keeping their equipment that has a limited shelf life working as much as possible.