I'm not confident that it would. There doesn't seem to be a clear connection between the transaction rate and the power use. That's not to say that the power use is or isn't "worth it" or whatever.
But, I think that one way the "energy per transaction" framing is misleading, is for exactly the "if you scaled up the transactions, the power use would scale proportionally" idea.
First, it isn't clear to me that it is even possible to scale up the transaction rate without either making the security worse or substantially modifying the design (or possibly both), but if you did manage increase the transaction rate, it isn't clear to me that this would impact the total energy use rate at all.
Well, ok, it might influence the power used by influencing the price or the issuance rate.
But, aside from that, I expect that the power use would be determined by whether someone profits by increasing the amount that they spend on power in order to mine bitcoin. This doesn't depend on the transaction rate.
Err, ok, I suppose technically if the transaction rate were higher, miners might get more transaction fees, and really the relevant thing is issuance rate + transaction fee rate,
but I suspect that the average transaction fee would decrease if the number of transactions were increased, so that impact should be small I think, because those two should largely cancel out.
Hm, ok, so if the transaction fees are determined essentially as an auction, what is the effect on the average fee per transaction, of multiplying the number of items (slots in the block) available per amount of time? I think this depends on the demand curve for transactions. I don't know what that curve looks like.
If we pretend that it is linear (just pulling that out of a hat. Though I guess if we zoom in far enough it should look locally linear, unless we zoom in too far and then it will look piecewise constant due to discrete numbers of people... whatever.), then, --- I should get back to work, shouldn't be doing this calculation right now.
But, I think that one way the "energy per transaction" framing is misleading, is for exactly the "if you scaled up the transactions, the power use would scale proportionally" idea. First, it isn't clear to me that it is even possible to scale up the transaction rate without either making the security worse or substantially modifying the design (or possibly both), but if you did manage increase the transaction rate, it isn't clear to me that this would impact the total energy use rate at all.
Well, ok, it might influence the power used by influencing the price or the issuance rate. But, aside from that, I expect that the power use would be determined by whether someone profits by increasing the amount that they spend on power in order to mine bitcoin. This doesn't depend on the transaction rate. Err, ok, I suppose technically if the transaction rate were higher, miners might get more transaction fees, and really the relevant thing is issuance rate + transaction fee rate, but I suspect that the average transaction fee would decrease if the number of transactions were increased, so that impact should be small I think, because those two should largely cancel out.
Hm, ok, so if the transaction fees are determined essentially as an auction, what is the effect on the average fee per transaction, of multiplying the number of items (slots in the block) available per amount of time? I think this depends on the demand curve for transactions. I don't know what that curve looks like. If we pretend that it is linear (just pulling that out of a hat. Though I guess if we zoom in far enough it should look locally linear, unless we zoom in too far and then it will look piecewise constant due to discrete numbers of people... whatever.), then, --- I should get back to work, shouldn't be doing this calculation right now.