The electricity will be reduced by the fact that Round 1 is not computing-intensive
Regardless of the complexity, if I use more power to increase my hash rate, then I will have a better chance of getting to the second round. Right? So, why wouldn't I use as much power as I can to get into the second round?
I think a solution would be to eliminate the PoW in the second round and simply make it a random selection (somehow). That would cut the expected block reward by a factor of N
2, which would cut the power usage in the first round by that same factor.
If you use more CPU power, you have always better chance to advance to Round 2. However, because Round 1 is not CPU computing, small players will be able to advance to Round 2 too. It is like we are giving more chances to small players to earn.
About your second point, let's me reflect on it.