We always taught "deepest dives first" because those profiles maximize allowable bottom time based on diving air and Navy tables - all that was available to us at the time. I bought an Edge shortly after it was introduced and was amazed at the difference in allowed bottom time, even above what we were doing with multi-level table techniques. Spent a lot of time listening to Huggins at various seminars, read everything available at the time, and did not find anything that led me to believe "deepest dive first" was anything but a method to maximize bottom.
Then came a trip to the Great Barrier Reef in 1990 - a 10-day liveaboard. We were forced to abide by what we called the Marquis of Queensberry rules of diving - some arbitrary depth limit, always deeper dives first, and no more than 4 dives in a day. We found ourselves lying to the DMs regarding depth. Our first dives were always to the maximum allowed depth - even if we only went 60'. That allowed flexibility on subsequent dives. Utterly stupid rule which we followed only in our reported depth, not our actual depth. We were lucky that computers were relatively new at the time and the DMs never checked them.
In practice, where and when ever possible, I still conform to deepest dive first and especially deepest part of an individual dive first. It just makes sense from a time-management standpoint. It shouldn't be a "rule," rather a best practice.