On the contrary, I've found that MWI is "usually presented" as continuous branching happening continuously over time and space.
Any links?
And (the argument goes) you can't argue against it on the grounds of parsimony
Indeed, the underlying equations are the same whether you aesthetically prefer MWI or not.
Sure. Here's one. LW's own quantum physics sequence discusses systems undergoing continuously branching evolution. Even non-MWI books are fairly explicit pointing out that the wavefunction is continuous but we'll study discrete examples to get a feel for things (IIRC).
In fact, I don't think I've ever seen an MWI claim outside of scifi that postulates discrete worlds. I concede that some of the wording in layman explanations might be confusing, but even simplifications like "all worlds exist" or "all quantum possibilities are taken" impl...
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.