Honestly I think no single system of writing is powerful enough to handle all the different versions of algebra. Mathematics can be extremely concise but only by constantly omitting stuff or overriding the meaning of symbols.

There are some happy accidents like df/dx making sense as both a derivative and a division of 1-forms, but on the whole you can't pick a single notation and hope for it to work well in all situations, yet that seems to be what most algebra systems do out of necessity.

To fix this I reckon we'll need to standardize not the automated algebra part but rather get those systems to communicate using some standardized format. Which is nigh impossible because of the sheer variety of mathematical concepts, but one can hope.