Great concept, but not sure about the claim that legal bills aren't "work product" - it depends on what they say. And it's quite probable that the most effective legal bills for data analysis purposes (i.e. detailed ones) would contain work product or attorney-client privileged information. When I was a practicing lawyer, I always redacted bills before filing them in court to support fee petitions.

Separate issue whether disclosure of the bill to you as vendor, with a documented expectation of confidentiality, would constitute waiver either of WP or A/C privilege. No obvious reason that disclosure to your service would be different than disclosure to TyMetrix, Serengeti, or Sky Analytics, assuming your T&Cs are well-crafted. But obviously check with your lawyers on that.

Also, purely from a business standpoint, you can bet that some lawyers will raise the confidentiality objection to discourage/resist adoption.

All is to say, the issue is an important one. Glad to see you're taking it seriously. Good luck!