I think that you have to take it in smaller "chunks" and set smaller goals along the way or a list that big will just get too daunting. I have climbed 390 peaks in Colorado with 300' prominence and the only "list" I have completed is the 14ers. All of the 13ers will be nice to get some day, but I don't look that far ahead, I look at them in smaller chunks.
I was in the San Juans when I hit the 1/3 point and was thinking about how many I still had in the San Juans and it was getting depressing, so I decided not to look at the list as a whole, but look at it in pieces. Recently I ticked the 200th one, now I am looking at some geographic goals until I get closer to 250, then 250 will be the goal and so on and so on.
Probably elevation and geography are the most common ways to divide out the overwhelming number of peaks into more manageable chunks - say the top 100, 200, or maybe all the 13ers in your county. That way you can reach little milestones that make you feel like you are getting somewhere, otherwise you feel like you are swimming against the current.
Right now I don't plan my goals out farther than what I can achieve in a couple of years. I haven't "officially" named all the 13ers as a goal yet. Its still too far out, for now the goals are more "target milestones" than completing a list.
I don't know if its possible to climb all the peaks in the world, but as long as you are getting out, having fun and exploring new areas I think ultimately you will find the chase satisfying even if you never finish "the list".