Procession-BoM is a hard-coded interaction. It does what it does because the Rulebook says so. IIRC (can't find the quote), Donald recognized that the way they should work, based on the wording of both cards, was too unintuitive, so he decided on this specific ruling, and that's how it is.
He really said that? Oh my, no wonder the "official" rule is so strange to me. Does anyone else know where he said that, maybe?
Here's a link to a summary with a link to the in-depth version:
http://forum.dominionstrategy.com/index.php?topic=8717.msg264712#msg264712Throne on Band as Feast would do nothing the second time via a literal interpretation (pointed out by Sir Martin). It seemed like no-one was ever guessing that, and it's not in the rulebook. So the ruling is that Throne Rooms "lock in;" and this doesn't ever matter except for Throne/etc. on Band as one-shot. The entirety of the special ruling is that Band is still Feast the second time; the rest of it follows from the rules.