Yes, there are limitations to MathJax, which is why I think the TeX filter needs updating, but there may be other ways to address what you are trying to display using MathJax...
In any event, once upon a time managing simulataneous use of TeX and MathJax was easily done, lol, by way of changing the tokens that MathJax uses, and there are a number of discussions in the forum explaining how to invoke and tweak those settings in AdditionalHtml. Moodle HQ argued that the current MathJax filter was heads and shoulders over the previously used methods and pushed through the MathJax filter so I would post a question to Damyon Wiese asking how the filter provides for changing the MathJax tokens Then..... you may wish to turn OFF the MathJax filter, add the text appropriate for your MathJax installation to additionalhtml (you will note that the CDN location may have changed for MathJax) and tweak your tokens (for example, using @i for inline and using @d for display. see the MathJax docs for more info. This will also allow you to easily add MathJax macros.
Now you can add what packages you want to the TeX installation, though some usages may still be impeded by Moodle in some cases. The TeX filter will parse the tokens identified in that filter, and MathJax will employ the tokens you have chosen in Additional HTML.
btw, it was unclear to me when Moodle rolled out 2.7 for Moodle.org whether use of both filters together had been fully resolved. You may want to ask someone at Moodle HQ where the docs are on how those filters interact in as much as I have been given to understand that be default they are set to use the same tokens..... which would suggest that the first filter in order of application would arguably suck up all the tokens and leave nothing for the second filter (unless of course the tokens employed were different.)
As far as construction tools, Moodle devs keep tying constructor tools to display technology, which has been deplored by most on this forum. In other words, constructor tools should be available in the editor without regard to what display tools you are using.
If Moodle devs made use of the new equation editor dependent on use of the MathJax filter then I recommend creating a tracker issue asking that they be decoupled (much as we had to do with dragmath when they did the same thing with respect to the TeX filter.) I am sorry that I don't have the specifics of that, but frankly I won't be bothered with that anymore.