I find that amazing. I think every app I've ever worked on or built with Heroku has tied into the API in one way or another. It's one of your best features.
To me, the API endpoints should behave the same way in a browser as with curl without ever redirecting to the login page.
But, once again, it might have been fixed in the meantime… I haven't tried recently.
At Pogoapp we basically reverse-engineered our API from Heroku's command line client, but it's excellent to have Heroku make the API public and formal, because it should make that process much easier and set up Heroku's API as a good target for other PaaS hosts to standardize on (in the same way Ceph & RiakCS have S3-compatible REST APIs)
There's lots of commercially licensed, self-hosted software (blog, forum, ecommerce etc) and hosted-as-a-service (wordpress.com, discourse.org, duelapp.com etc) etc that would be applicable.
Enabling that by API or in general would be awesome.