I'm confused by what you mean when you refer to "my notation" -- ostensibly that should mean MathML (which, for the record, I did not create in the slightest), but then you go on to take a swipe at the caret, which is not MathML at all.
In the first paragraph, you seem to be saying that TeX, like MathML, is semantics-free, which is true. Presentation MathML and TeX notation are equivalent there. Don't forget, though, that MathML also encompasses Content MathML, which as is explained in the 3.0 docs, is aligned with OpenMath, which *is* a semantic encoding. In *all* non-semantic encodings, it is always left up to the reader to "interpret the damn thing" (and there is nothing you as an author can do to prevent someone, somewhere, from misunderstanding you). The same is true with words, is it not?
But I'm also confused by what you're trying to say in the second paragraph, where you appear to being knocking MathML again, this time on the grounds that it is not connected to the "real world" (meaning, apparently, solely printed books and journal articles?). It is clear, is it not, that MathML is a _web_ publishing technology? The syntax is inherited from HTML, and you're certainly free to love or hate HTML, but its regularity is what makes things like the linking and CSS styling mentioned earlier possible.
I'd suggest you take a look at Mozilla's MathML "demo" pages for a more detailed discussion on how MathML's alignment with HTML and the DOM make it a superior fit for publishing mathematics _on_the_web_. There are more examples there than I had room to discuss. No matter how much you love TeX, you can't enable tooltip-style hover annotations in a printed & bound manual -- even if it was typeset with TeX. I'm not sure you could embed a link in the middle of a TeX-formatted equation in any CMS currently supporting the format, but I wouldn't want to be the first one to try it.
Finally, like most of us I have endless respect for Donald Knuth, but let's not let that cause us to fall into the trap of pretending that TeX's mathematical typesetting is free of errors or the need for manual adjustment when expressing a complex equation or notation. In particular, when it is left to automatic, TeX often chooses less-than-ideal sizes for tokens in multi-level stacks or continued fractions, and as Mozilla documents on the <mo> tracking page (here: http://www.mozilla.org/projects/mathml/demo/mo.xhtml), TeX is only capable of producing symmetric fences.