When you write web-pages, do you usually write the raw HTML or do you use something like Markdown or Wikitext and have it converted to HTML? If the latter, then why would having LaTeX as part of the input and MathML as part of the output, be any different?
Also, directly converting TeX to MathML, even client-side, is much easier and faster than MathJax's many-to-many approach (I'm not criticising MathJax — given the constraints, they're doing the best possible job).[0][1][2] (See also the Ascii to MathML converter[3] that has already been mentioned in another comment.)
Most people who write for the web probably do indeed write in something like markdown, which means they probably sprinkle in a bit of HTML for the parts which markdown doesn't natively support. I imagine a lot of blog posts written in markdown contain a few <table> elements, for example. Anyone writing math content for the web using markdown will have to either write the mathml directly, or write the math expressions in another language and manually compile it to mathml which is copy/pasted into the document. Maybe the CMS they happen to use will some day add native support for compiling latex, but that sounds rather unlikely.
Pandoc and Mediawiki have been able to convert embedded LaTeX to MathML, for a while. Once Chromium supports MathML most CMSs will probably start providing suitable converters, and in the meantime MathJax will still work (and better, since MathJax's Native MathML output is faster than its CommonHTML one[0]).
Think of MathML more like SVG. You can write it by hand (and in some cases you should), but in most cases you should use a graphical editor (like inkscape), or a library (like D3).
This is exactly the property that makes it actively worse than TeX notation. It makes equations a second class citizen compared to text because you can’t write them comfortably without external tools. MathML is a failure - because of its ludicrous verbosity. The correct solution may not be TeX notation, but it can’t be this bad a step backwards in usability.
In either case, you can use TeX as your input, and if you do, you have to convert it, client-side or browser-side, into something usable by the browser; it's just that if the browser accepts MathML the rendering is faster and/or more convenient, plus you get other options.
Sorry, my claim was about the two notations: that the TeX one is writable, and the MathML is not.
I’m not claiming that a JavaScript parser and complete renderer for TeX is better than a JavaScript parser that renders via MathML. The second option may indeed be more efficient - but making the browser parse a sensible notation for maths instead of an XML crapfest would be better than either.
I don't see why rendering TeX formulas would be slower than rendering MathML. It should be possible to maintain implementations for both variants with similar performance. MathML's parser should be simpler though, cause it's XML, which already has many efficient parsers.