Some of the system tasks need to have the context - so they cannot be processed by external service. Just like in this case. Then, you need to keep in mind how the scheduler works and also what is it's reliability. By default, the automatic scheduler is used in Kentico 13 (older versions were using the request mode by default). But still, the scheduler used by the Xperience administration and live site applications runs within the ASP.NET process, so tasks cannot be executed if the corresponding web application is not running. So, you would need to ensure the application is always up and running (AlwaysOn setting in IIS does not mean that IIS will start the app in case of some failure or error just so - it will be started on the first request). So, therefore it is recommended to use some service which will periodically make a request to the admin app (to the admin domain or /admin path).
Also, in this case the task needs the Kentico admin app context, so it cannot be executed within the live site either.