This is a nice and unexpected kind of reply indeed. :-)
I'm imagining a view where the owner of the calendar would define their available time, in a manner of regular schedule and one-time exceptions. The calendar would remember available / unavailable times and booked / non-booked times (these would be orthogonal since we want to let the owner accept a booking even in a time where they said they're not available).
Another view would show the calendar to the public where visitors would see when the owner is free (= available & non-booked). They could then choose a timespan to book along with their identification (name, e-mail) and optionally a short message. This would make that time, say, "tentative". The booking would show up in the owner's calendar and a notification would be optionally sent to them. The owner would then either reject the booking, which would cause that time to again show up as free or they would accept, which would cause that time to show up as taken.
This would be the basic functionality. I also see room for enhancements. The owner could define minimum breaks between bookings. Say they would set that to 15 minutes. Then, if I booked for 12:30 - 14:00, the calendar would show me as taken from 12:15 to 14:15.
Another enhancement could be for the client to provide a password, which would enable them to cancel a booking they had previously made.