I should clarify (I'm aware that you said you don't have an alternative). My question is of what type/form the alternative should take.

I think that a new paradigm should try to achieve the following: 1) Be based on code that can be machine interpreted and used afterwards in computations. Maybe this will require a more standardized way of writing math (like the apl that was suggested). 2) Be based on source code that is not cluttered and can be read easily by a human (maybe like markdown) 3) Most important of all: Formatting should be a completely independent layer. My original equations should have nothing more than math, it should be the renderer's business of how to present it to the consumer (webpage, pdf or whatever). It should be very easy for example to change the alignment of your equations a-posteriori without messing with the equations themselves.

1 feels too restrictive. I'm not sure how easily it would allow for writing math that isn't yet amenable to machine computation. Just as a random example, what if I'm doing some Étale cohomology stuff, maybe throw in some stacks and whatever else. How impressive would this code have to be?

We can have multiple "interpretation modules" and for some fields these will produce more useful output than for others. Currently, you cannot even attempt at doing so since the tex equations are typically polluted with formatting related code.