Very interesting. If everyone submits a couple of times or even ranges of times when they are free (I'm free Friday between 10am - 2pm except an hour for lunch) then you could use schedule.js (
http://bunkat.github.io/schedule/) to automatically suggest the best date and time that works for everyone (sort of like how the newest version of Outlook works).
If you had access to everyone's calendar, you could automatically suggest all available times instead of needing people to propose times and end up with exactly what Outlook does.