See my comment above about my experiences with this: I tried, and a corner case killed me. There’s a reason why Mathematica and other CAS packages have invented their own idiosyncratic notations. LATEX and MathML are truly hopeless when it comes to communicating with algebra systems. It looks deceptively ’doable’, but really it’s a recipe for disaster.
1) assume a standard interpretation of symbols (e.g. this site uses a-g for scalars, h-z for vectors and A-Z for matrices) and make those assumptions explicit and modifiable (e.g. WolframAlpha displays "assuming X is a Y, use as a Z instead").
2) Support only the subset that MathJax can handle, which seems to be enough for most purposes.
I definitely agree that LaTeX is not the optimal input format for that purpose, though.