In mine, none. In yours ... ?
A santoku isn't a traditional knife at all, and there's no "classic" slot or role for it in a professional's block. It's history, such as it is, is as a sort of housewife's do it all. It's a cross between a nakiri (itself, the play-at-home version of a usuba), with a kamagata front end, and a gyuto/chef's knife edge and belly profile. The santoku's shape and length compensate for naive knife technique. The knife is easy to point, because it's short. Hard to hurt yourself with, because of the sort of sheep's foot point. Has plenty of knuckle clearance, and so on.
Despite lacking a classic point, most of them actually have an edge and belly arc similar to a French profile (as opposed to German profile) chef's knife.
Some people with good skills, mad skilz even, just plain like them. I don't see their appeal and find them a sort of personal knife mystery; but I have a little 7" "Nogent" chef's knife which, while it isn't my go-to gyuto, I'm quite fond of. I bought it (and use it mostly) for shallots and other very small vegetables, and as a kinda-sorta deba for small fish. However, sometimes it gets used, "just because," even though it wouldn't usually be the first choice. Breaking small birds for instance.
Discussing knife technique, even from the perspective of "no more than one or two right ways to do anything," is difficult because there are so many tasks; some of which have specific techniques associated and some of which do not.
For instance, a santoku certainly can be used in the same tip/fulcrum fashion as a chef's knife described by Chef Todd, because it's edge and belly profile are very similar to a French profile, minus the point and, depending on the individual santoku, perhaps some of the belly. But there's enough.
Furthermore, classic "chopping" is not a single task, but several discrete operations: blocking, planking, sticking (alumette, batonnet, julienne, etc.) and dicing (medium dice, fine dice, brunoise, etc.). Blocking and planking anything of size requires lifting the knife entirely off the board. For that matter, so does dicing if the cook is pushing large piles of sticks under his knife. There's a limit to how high you can comfortably raise the handle with the tip on the board.
There are any number of ways to teach skills; but most of them have a few commonalities. The knife is held square to the board and square to the food. The spine is held in line with the forearm, as though it were an extention. And, therefore the tip is an extension of the forearm also. A chopping knife is gripped in such a way (almost always the "pinch grip") that the knuckles face out instead of down, making it possible to chop with even a fairly narrow profile without rapping the knuckles against the board. So, you can see that if you have skills, nearly all of the rationale for a santoku disappears.
Good skills mean you can use a more versatile and less naive tool; but they don't mean you have to.
It is definitely true that Asian cooks using Asian knives and Asian technique tend to "push cut" (straight up and down) in a constant noisy tap-tapping. While those of us trained in a French or "Continental" technique tend to use more of a compound shearing/sliding motion and do keep the tip on the board when we can. German profile knives with their greater arc are better for rock chopping than French profiles. Personally I prefer the French -- German style knives seem heavy and clumsy in comparison. There is no best it's simply a matter of taste.
Just like whether or not you choose a santoku. Because I don't like them, doesn't mean you shouldn't.
Good luck on your continuing knife journey. You come up with interesting ideas and ask great questions.
It's fun travelling with you,
BDL
