Just curious, does anyone know of a company or software that uses AI or machine learning to analyze complaint data?

Not AI, but it's pretty easy to write text mining code to identify complaints with high risk terms. I've also geocoded and proxied complaints data and used fair lending tools to identify patterns that correspond with complainant demographic or neighborhood characteristics.

CN, outside of some of the largest banks, most complaints should be reasonably manageable.
Correspondence from regulators, agencies and governments first, attorneys next, customers then non-customers.

Within each category by product or department. Also a column to indicate if discrimination (or difference in treatment) is noted.

For lending, try to identify, GMI and location, like InFairness indicated. Also, distinguish types of complaints. They ran out of donuts last Friday, or the bank returned my check is a lot different than a claim of discrimination. Some are service issues, not what many banks would consider a complaint

Prior to the CFPB essentially adding proxy GMI to complaints I would have shied away from such a practice. But since the Bureau has done it, I come down to the best defense being a good offense - so knowing your numbers is recommended if not a best practice.

I like the idea of doing it in-house. I see fair lending becoming a bigger deal this year and in the few years to come and would rather keep it in-house or thru counsel as the data is protected that way. I just resist putting sensitive info in a vendors control.

Lastly, if a vendor discussion develops this will have to be moved to a private forum.