This part is already done. Admin users can generate the reports every time they want, they can also see the status of previous reports and tweak their configurations.
The situation we are facing now is more like: what if said users never send the report. They don’t care about it, they simply forget or they find the sending instructions too complicated (I would argue this is not the case as it is as easy as going to the /admin tab, but I’m not a regular user). The point of the survey report is that as a software community we have regular data that is aggregated and anonymous. We could send some messaging every so often asking operators to send the report. But it is a tossup if they will answer.
To the broader point of having some tasks that start from the server I agree that this could be a red flag sometimes, but I also think we must start by acknowledging that the edx-platform already has this behavior written in. By not allowing the platform to start some tasks by the server we are not making the architecture better, we are only making entire features not usable. This applies to the email nudges and the SAML certificate verification (that I know of).