I'd love it if I could see details/data of people across my whole tree. For example, in a given year, which of my ancestors were alive (like 1864, to see if I've captured civil war details of everyone who was involved), or where they were located at that time.
It would also be fun if you could display demographics of the family tree, like who lived to be the oldest, who had the most kids, got married the most times, etc. This is all based on information already in the records, so it's just a matter of displaying it in different forms, but in ways that make it more fun.
I studied social history in school, so in addition to being very conscious of how families and communities build their own history, I'm also still annoyed at how insular history is taught, and I think genealogy is an excellent medium for seeing connections, both with the past and with the present--refugees, for example--did my german ancestors voluntarily leave their homeland, or was there something locally or globally going on at that time that might have encouraged them to leave? Likewise, the Enclosure acts in the UK, and the Famine in Ireland, and religious intolerance all over the place. I just think the potential for making sense of things is enormous and unexplored from this angle.