Hello! There are actually some researchers that use BAML! Well, at least one.
Why do most labs not use BAML? Likely the same reason most app developers don't use BAML - they haven't heard of it, they haven't tried it out, or they don't want to take another dependency.
BAML is beginning to spread by word of mouth, but we aren't mainstream yet, so for most developers and researchers, it just isn't a tusted entity. Academia also tends to lag behind industry a bit in terms of tech tooling adoption.
That said, BAML is a GREAT fit for a lot of research, given the way parameterize prompts and make testing easier. I've done my own needle-haystack tests in BAML, and found it very handy. Another selling point is the fact that you're likely to do research on smaller models, and you don't want your results to be confounded by the fact that smaller models have a harder time producing valid JSON. BAML releives you from this confounding effect by providing a more flexible parser and a prompt that's easier for small models to follow, compared to the JSON Schema based frameworks.
Great question!