That's a slightly different issue from what this study was about. Specifically this was looking at grammatical structure that's unique to legal documents rather than specific vocabulary choices (I.E. jargon). Legal documents tend to have both, a unique hard to understand structure, as well as using words that are both uncommon as well as have unique definitions in the legal context that are different from their common ones.

I suspect jargon is a problem no matter what, every specialized field suffers from that to a certain extent, but the unique grammatical structure is a problem that's really only seen in legal documents. The explanation for why that's the case seems to be potentially a historical accident and basically boils down to "because that makes it sound legal", despite literally everybody saying they prefer legal documents written in a normal style.