Structural markup and semantic markup are separate things, IMHO. Structural markup means that you don't abuse tables and instead use divisions to organise a page (as an example). Semantic markup means you use accurate element types to describe your data. They are similar concepts, but not identical.
"Case in point:" the I element type vs the EM element type. One means emphasis and the other means italics. It's arguable that the I element type should not have remained in HTML, but the argument for keeping it there was that there is a strong case for where italics is a convention that should not be broken; for example names of different species in biology texts.
If I wanted to index a website for search purposes, then ranking the keywords within EM elements higher than normal text would be sensible. The same is not necessarily true of I elements. There are a number of search engines that behave differently based upon whether they encounter I or EM. I consider this to be a feature rather than a bug - after all, I means a completely different thing to EM. The only reason they are confused by authors is because the presentation in common browsers is the same.
The difference between STRONG and EM is a matter of degree - there have been arguments that STRONG is redundant and that it should be replaced with nested EM elements. EM == emphasis. STRONG == strong emphasis.
"People think about these mediums visually,"
I don't. You'll have to prove that assertion rather than simply say it and hope people believe you. If anything, I experience what I write aurally rather than visually - I'm sure I'm not the only person who writes with a tone of voice in mind rather than how it will look on the page.