Re: Amok Time doesn't make sense.
One really wonders how much of this ceremony would have been part of routine pon farr management for the average Sjoek and T'Jane, and how much was unique to
a) a member of the exalted family of Sarek (or T'Pring's no doubt equally exalted lineage)
b) an inhabitant of Shi'Kahr, a potential backwater with quaint folkways
c) a member of the strange cult that still practices telepathic bonding against modern Vulcan ways
I really doubt every family could afford such an arena. And we didn't exactly see more than one next to Shi'Kahr - is it a single-family town, if not literally, then in the old Western style of being utterly ruled by the Boss Man and his sons (or perhaps the Boss Lady and her daughters)? Is T'Pau perhaps a native of Shi'Kahr? Is she a member of Spock's family, or T'Pring's, or even both?
Quite probably, all Vulcans take their pon farr shame to as distant a location as possible. Perhaps Shi'Kahr, on the edge of the desert, is a popular site for sex tourism because nobody goes there for any other reason? And Sarek's family just runs the ancient grounds for a variety of customers.
Spock mentions that the arena has been in his family land for two thousand Earth years. In that time I would imagine that his family has grown quite large. I imagine that it would be used for first marriages, such as Spock and T'Pring or Sarek and the mother of Sybok. Sarek's later weddings to Amanda or Perin were probably much less elaborate affairs. If each member of the family (or just the males as T'Pring is not at her family's shrine but at Spock's) on;y uses the space once in a lifetime it could be used by thousands of members of Spock's family over time. We may cut off our definition of family at Second or third cousin. Vulcan's may big much larger. In Yesteryear Spock impersonated a cousin and Sarek didn't recognize him but accepted him at his word. When your family numbers in the tens or hundreds of thousands you may nor be able to know even a fraction of them. We don't even know that the city in the background is actually Shi Kahr. It's based on the appearance from the animated series but it may be a typical design for cities of that size. Vulcan cities may be much more homogenous that Earth cities. Spock's family may have fist settled there but they are now probably spread all over the planet.
We can admit that we're killers ... but we're not going to kill today. That's all it takes! Knowing that we're not going to kill - today! - Kirk - A Taste of Armageddon