I think you are right that good feelings and status are a big part of it. Why do people endure all manor of inconvenience to be a part of any big event, a movie opening or concert or rally? A lot of bragging rights to have been a part of something, rather than just watched it on TV.

Still I wonder if that is the whole explanation. The system needs X% of voters out there to be viable, but it has no real carrot to attract people to vote. So then voters just assign a value to voting, and show up in relatively large numbers on their own. And it all works out? It's a very clever arrangement if that's how it works.