See my comments here. https://moodle.org/mod/forum/discuss.php?d=259642#p1127624
Yes, I agree with your analysis (it is essentially what I argued as a basis for not rolling out the MathJax filter, especially as a default, at the present time) but it looks to me that the power on high has already made some decisions (whether they are aware of the impact of those decisions or not.)
Based on what has transpired in the last few months, I can see an argument for a TexLive filter for those with TeX needs beyond those that can be addressed via MathJax, which is a narrow band I would think of largely University level Math users relying on extensive macros or packages not supported by MathJax.
The current TeX filter can serve that need, especially if it is needed to support the Algebra filter, which is still in use by lots of Moodle around the world. But one thing that has to be resolved is whether the Algebra filter can be successfully decoupled from the TeX filter (so that the results of whatever the Algebra filter does is past agnostically to any TeX parser.
And that of course is one reason why a MathJax preprocessor for ALgebra notation could be handy, as it eliminates the need for a perl distro (though arguably most linux/unix based systems will have it anyway), consolidates the tools used for most Moodle SAs and users, and frees the TeX filter to be what it needs to be without having to address the needs of those who really are not interested enough in Tech to bother.