Nicely written, well thought out, and just plain wrong!
The notion of search engines using “themes” is a fantasy in my opinion. I have never seen any evidence that suggests that search engines, Google, in particular, ever look at “website themes” and all evidence I have seen indicates they do not. I think your post has simply blended a few partially true concepts with a bunch of hogwash.
I’m sorry to be so critical, but if you can provide a credible source for your information, perhaps I can be converted.
The notion of “site relevance” is not supported by any papers published by Google’s founders nor any other credible research that I have seen. You are correct in your assertion of it not being important. It’s not important, in my opinion, because it simply doesn’t exist as a factor in SEO.
Search engines index individual web documents, not websites. This is fundamental to understanding how search engines work and the fact that you devote so much of your discussion to “site themes” and “site relevance” indicates that you know very little about how search engines actually work.