It's hard to design a proof-of-work scheme that is both secure and performs "useful" work.
Then it is not a useful monetary system. When people trade money (paper or electronic), they are trading time they invested in doing useful work for someone else. When bitcoins are traded, you are trading wasted computer cycles.
The computer cycles are useful: they secure the network.
But you're both completely missing the point that mining for coins will become exponentially more efficient over time, with new mining techniques and hardware.
When more energy-efficient mining equipment is created, people buy enough of the equipment to use the same amount of power that they used to have. For example, one might replace a 300 W GPU with a 300 W ASIC miner. The total amount of mining is determined by the exchange rate; since the exchange rate is expected to increase due to deflation, the amount of power spent on mining is also expected to increase dramatically.
I may not be an economist, but the method used for mining seemed.. illogical to me as well. If a bitcoin was released into the wild based on running real world problems like folding@home or something else it would have much more sense to me.