I don't think enough people appreciate (or understand) your point 4. I am fairly good at algorithmic optimizations and pretty good at your implementation optimizations, but I do not have the math to do much mathematical optimizations, so spending any time on these kinds of problems gives me a visceral understanding of your point 8.
But I've talked to too many people who don't understand that such problems exist, and therefore don't see the point of any optimization (and then wonder why others consider their products to be hideous monstrosities), or believe that micro-optimizations or algorithms are the best you can do. In reality, all three are closely tied together and, in fact, applicable to almost any problem.
Your points 6 and 7 could be elaborated more. Or at least stamped on the foreheads of some educators of my acquaintance. One of the things I learned from what math education I have had is that you won't really understand something without seriously using it.
I hope that this was actually part of your PhD research, or if not that it didn't delay you too much. And if you're out in the "real world", all you have to do to succeed is to forget you ever heard of your point 10.