Be really specific.
What exactly is it that you can't do in a shader, that you can do in a CPU based sandbox, better and faster?
(There are things, sure, like IO, networking, shared memory but I'm struggling to see why you would want any of them in this context)
I'll accept the answer, 'well, maybe you want to render fonts on a toaster with no GPU'; sure... but that having a GPU isn't good enough for you, yeah... nah. I'm not buying that).
Even if you already have a GPU renderer for glyphs and any other vector data, you still want to know where to actually position the glyphs. And since this is highly dependent on the text itself and your application state (that lies on the CPU), it would actually be pretty difficult to do it directly on the GPU. The shader that you would want should emit positions, but the code to do that won't be easily ported to the GPU. Working with text is not really what shaders are meant for.
But again, this has nothing to do with HarfBuzz or wasm.
slug builds acceleration structures ahead of time. the structures are overfit to the algorithm in a way that ttf should be but which is economical for video games. that doesn't seem like an interesting concern and nothing about it is specific to the gpu
1) Because SDFs suck badly (and don't cover the whole field) when you want to render sharp text. SDFs are fine when used in a game where everything is mapped to textures and is in motion at weird angles. SDFs are not fine in a static document which is rendered precisely in 2D.
2) Because GPUs handle "conditional" anything like crap. GPUs can apply a zillion computations as long as those computations apply to everything. The moment you want some of those computations to only apply to these things GPUs fall over in a heap. Every "if" statement wipes out half your throughput.
3) Because "text rendering" is multiple problems all smashed together. Text rendering is vector graphics--taking outlines and rendering them to a pixmap. Text rendering is shaping--taking text and a font and generating outlines. Text rendering is interactive--taking text and putting a selection or caret on it. None of these things parallelize well except maybe vector rendering.