I did get some feedback from R&D on these questions.
Unfortunately, it is operating as expected.
Generally, these API calls will only show the contents of explicitly configured routes.
The interface is only shown if you configure a route with an explicit interface as the destination.
Interestingly enough, when you use show-routes-static, the interface for the default route is included in the output.
You can see an example in the API docs: https://sc1.checkpoint.com/documents/latest/GaiaAPIs/index.html#web/show-routes-static~v1.7%20
It seems like the other API calls for different sources of routes (e.g. show-routes-bgp) includes interfaces in their output.
Which suggests they might be more suitable for your intended purpose.