Not the original poster but here is why I don't use LaTeX. You have to compile to see your changes, and LaTeX does not have a wysiwyg mode. (There are a few attempts, but none of them that I have tried work al that well. and I have used Lyx a lot)
Courts have rules that are based on typewriters and word perfect. You must have your heading on line 8 or line 10 or what ever it is for that court. From my experience LaTeX and Lyx is that creating a style sheet and tweaking it is actually rather tedious and time consuming as there are no tools to my knowledge to get you to the 90% done format quickly.
Further more I don't know of any good way of collaborating with people using LaTeX. git is fine for coders but it is a bit of a nightmare trying to get non-coders to share free form writing with it.
Admittedly these are all things that could be addressed with some UI polish and some small tools. but If you need to get something filed by a deadline, the best way is rarely the path you take, but rather one you know you can complete the task on deadline.