Hello,
Yes you are right. In Agile team can pick-up when they free. Howerver, practically team divide Stories and dig-down to perform detailed analysis/estimates. The most efficient way is to have something finish everyday ( story/task ). So it is good to have ownership of someone, and then if you want to work/help on that item, you can just ask for pick-request. The owner has to grant / project owner can grant all request. Hope this will address your concern.
– Krosswall team