This would be an awesome feature to have! I think that providing developer access to the credit data would enable all sorts of new ways to sort by writers, producers, labels, etc...
I think it's always super cool to see who worked on a track behind the scenes and I think that it would be really awesome to do some data analysis of which entities are responsible for production in certain areas of music using the API (including the most popular songs in those areas). An API layout like @DiFronzo suggested would be great. I would be first in line to use this data if it was provided!
p.s. I know I can probably find it all elsewhere if I looked hard enough but having it in the API would be super convenient instead of having to scrape other sites
I work at a major and we need to find all of our writers' appearances on NMF - something that's done manually at the moment. Using the API could hopefully automate this and save a lot of time (and increase accuracy).