Pick-up and deliver mechanics are a great way to entice player interaction within a round of turns, without having to use real time mechanics. You can create delayed responses which add weight to player decision and it encourages players to think a few phases in advance. A game that does this really well is Merchant's & Marauders by designers Kasper Aagaard and Christian Marcussen, where inventory is transported across oceans to ports for trade and seized by marauding pirate opponents. Other's can be found in this comprehensive list of games on Boardgamegeek.com (BGG).
The pick-up and deliver mechanisms in Floating Floors that are intertwined with the recycling of resources, act as a catch-up mechanisms and encourages team member discussion at the table.
The challenges of a pick-up and deliver mechanism are that it can be tricky to balance the feeling that an opportunity to pick-up and deliver feels earned for, while also retaining tension by limiting the chance of runaway leads.
Some ways I've tried working in pick-up and deliver mechanisms have been the way jutsu are handed off to the next player, the bonus jutsu everyone else at the table gets when you store chakra and the recycling of previously placed jutsu. All of this also has a risk-reward system where players must decide whether the risk of incurring a penalty is worth the reward of potentially acquiring further jutsu tokens and sabotaging the path of your rival.
What games have you played that have examples of pick up and delivery mechanisms. What did you like about the pick up and delivery mechanism? Did it seem purposeful and intuitive or just an extra reason to reopen the rulebook "every now and then"?