@toucan , A little correction to your understanding. "Custom" container can also run on App Service Plan along with Premium.
But it's is not available in Consumption plan yet and the statement in the document you are referring still holds true. Also, currently there is no plan to add this support in consumption plan.
But we would like to know more about your need to use custom container. Is there any dependency or something missing in Function Host which is needed by your app that made you to go for "Custom" container?
UPDATE: Thanks for explaining your scenario for the need of custom container. One cost effective solution to this can be use Logic App and Azure Container Instances together. It will be like:
- Deploy your container in Azure Container Instances.
- Use Logic App ACI connector to start your container group when needed and then stop once done. For details on the connector, refer this.
- The above action can be scheduled using a recurrence trigger in Logic App.
Since Logic App charges you for the action run (pay-as-you-use), it will bill only when your schedule runs per day. And for container instance, you will be only billed during when you run your container since every time you are stopping once done.