As if a plain vanilla SharePoint installation wasn't bad enough, where I work we have documents spread across: SharePoint, Lotus Notes, Gmail for Business, Google Drive, Google Apps, shared directories and more.
I don't recommend you try this unless you are a lawyer already who can somehow turn this startup into a legal battle, and make profit that way. Good luck...
We are tackling Life Sciences as we speak.
As for startups taking this on, there isn't a chance in hell. The problem is too big to solve quickly enough to get market traction. SharePoint is big and complicated for a real reason.
Actually, all you need is a better salesperson. Sharepoint is sold by salespeople to people who have no idea of what they are buying.
How is this any different than people emailing files around (which legal departments still do themselves quite a bit)?
What gp described just seems inefficient in general.