Are even regular scheduled mail checks too "expensive" on mobile for you? Slow mobile connection, too much traffic, 
Use cases:
1. While roaming (say internationally), but when one account is still important for timely messages, while the rest aren't.
2. When there are many (secondary) e-mail accounts that aren't that important, and you can read them once per day. Yes, one can set them to sync once every 24 hours.
3. When you have
high-volume (but low-importance) accounts that you don't want to sync on mobile network, and you are on the road for a large portion of the day, especially when you are traveling in rural area with limited network bandwidth that you need for other, more critical at the moment communication (e.g. connection to navigation/map servers).