Not without a trusted central party you couldn't. The work that goes into bitcoin mining is the 'distributed engine' that prevents double spending or forging of bitcoins. Bitcoin mining is not just a way of handing out new coins, its the very engine of the whole system. The only known way to break that engine is to control a bigger engine of the same spec (the >50% attack), and thats looking increasingly unachievable by anyone.
Bitcoin couldn't and wouldn't exist at all without that promise. So a simple system based on allocating 100 coins to everyone just wouldn't do at all.
The 'work' is actually the verification of transactions on the blockchain - the reward from mining is just an incentive to do this (mining & verification are tied up in the same process).
The energy expended in mining is necessary to validate transactions in the network.
You might be able to make it more energy efficient but you can't remove the energy expenditure.
Ideally, the BOINC processing would somehow be directly integrating into the mining itself. But again, I don't have any idea how that could actually be done. But it would be nice if that is possible.
I don't see how it is not the case that mining Bitcoins is throwing away energy.
If someone had made a crypto currency based on, say, protein folding [1], I could get behind that.
We could just create a crypto currency where we just hand out 100 units to every person. That certainly wouldn't require ASIC farms and such.
[1] Yes, I realize that the whole 'hard to do, easy to verify' bit is not completely obvious in the case of protein folding or SETI signals.