I like your story, but if you're using it to make the case for spanking in particular, I think you're missing part of the bigger picture: Those kids in the restaurant were not bratty because they weren't spanked. They were bratty because their parents completely tolerated the bratty behavior, as if there was nothing wrong with it. Their parents could have used your advice not to think their kids are perfect...they were definitely in need of discipline that night, and their parents honestly should have nipped it in the bud much earlier than that night...but did they need to use spankings in particular? Not necessarily. I've seen lots of kids who act like that, and the common thread is that their parents simply shrug it off and let it pass, and they don't address the behavior with any level of seriousness.
I like how you mentioned that some kids have an iron will and a rebellious streak and might need spankings, too...but coming from my own experience of having been one of those kids: When your kids do show an iron will, it's worthwhile to assess whether they might actually be in the right in the first place. If they are in fact on the right side of the confrontation, it would be wrong to force them into submission simply because you're bigger than they are and you can. It's probably very unlikely for a six-year-old to be in the right, but...as kids grow up, it might become more common.
Now, the "Do not speak unless you are spoken to" and "Children are meant to be seen, not heard" rules, on the other hand...I've always considered those ones to be pretty fascist, because they're predicated on the assumption that children not only have nothing worthwhile or interesting to say, but that they're literally
less important than adults and unworthy of interaction.

In general, adults who have that particular rule are selfishly using their authority as parents to subjugate their kids, just because it suits them. "Might makes right," I guess. If the point is just to keep kids from being boisterous, a better rule might be, "Do not be loud and inconsiderate, do not whine, etc.."