Please don't flame me, I'm just spit-balling here.
Could the blockchain size problem and the lost coins problem both be solved by the following solution?
Change the protocol so that the client nodes only keep the last x years of blockchain history. As blocks with coins that haven't been moved in x years fall off the back of the chain, those coins are added to the next new block's mining rewards.
I don't really understand the protocol well enough to know whether a change like this would even be possible. Comments?
How many years? Who gets to choose? I vote for 10,000,000 years. I'd hate for someone to choose a number like 40 years. Just think, a 20 year old sets aside a bunch of bitcoin for retirement today and stops paying attention to bitcoin. A year later the system is changed to re-issue coins more than 40 years old. When he is 62, he goes to access his coins and they are gone!