Another use case for service workers in the extension context is using the Push API which is only available in service workers.
Bug 1344561 Comment 10 Edit History
Note: The actual edited comment in the bug view page will always show the original commenter’s name and original timestamp.
Another use case for service workers in the extension context is using the [Web Push API](https://developers.google.com/web/fundamentals/push-notifications) which is only available in service workers.