The amount of energy used for Bitcoin mining has very little to do with the rate of transactions. The limiting factor is mining profitability, which depends on capital and energy costs on on hand and current and expected Bitcoin prices, the block reward (which decreases over time), and transaction fees on the other. Only the transaction fees increase with more transactions, and for now they're insignificant compared to the block reward.
A billion Bitcoin transactions would be about 250-500 GiB, depending on the transaction size. If we were willing to accept block sizes of 1.5 to 3.5 GiB then we could handle that many transactions per day using no more energy than the current system. Of course, you'd need a 50+ Mbit dedicated downlink and some fairly capable hardware just to keep up with all the traffic, which is why we don't permit such large blocks.
A billion Bitcoin transactions would be about 250-500 GiB, depending on the transaction size. If we were willing to accept block sizes of 1.5 to 3.5 GiB then we could handle that many transactions per day using no more energy than the current system. Of course, you'd need a 50+ Mbit dedicated downlink and some fairly capable hardware just to keep up with all the traffic, which is why we don't permit such large blocks.