I reviewed Slate for one of my clients' private APIs. We ended up using Postman's API docs instead. The logic that brought us to that point were:
1. The ability to generate/sync documentation from a Postman collection meant we could write our test suite and documentation in one step.
2. Since we were already paying for a team account, adding Postman documentation was practically free.
3. Environment variables. We could write our test suite with one set internally and then publish our API docs with another set.
As someone else pointed out, it's possible to generate Slate documentation from an OpenAPI spec, but to me Slate on its own leaves a lot to be desired.