The fact word offers a competing feature does not mean this is not a pain point people would pay money for.
Have you tried to use Word's features as part of a mid-size team to manage a complicated document being edited by multiple users? Word's merge is crap.
My old law firm used version control software that appeared to be straight from 1991. So there's plenty of room to solve real problems here.
OP, I wish you the best of luck. But I concur with others, the use case for this product I see is for a team or company to learn to use it internally, not for a bunch of lawyers to use it across firms. So, keep the free tier to attract people who are willing to use it on their own (or in case someone can convince those outside their organization to sign up in order to participate on projects), and then increase pricing to any sort of team.
Also, I'm sure my firm could never have used a cloud-based solution, regardless of security, because we probably had clients who would not allow their information to be stored in the cloud.
Also, because I can speak to lawyers, the diffing needs to be excellent and it needs to be easy to create and share redlines in the ways lawyers are used to (send as a word doc/PDF, etc.). Perhaps this is already there, I'm excited to check it out.