There might be possibilties that this is a requirement for many business users. Can you develop a Flow template that will save attachments from shared mailbox into a SharePoint document library on Daily or weekly basis only (not when each mail arrives). I know there is an option to use trigger "When a new email arrives in a shared mailbox" & then use "Apply to each" along with "Create file". But it is running on every mail arrival. I need to create a custom Flow that trigger on 00.30 AM and check all the mails of Yesterday inside shared mail box and save the attachments from all the mails to a SharePoint online document library inside a folder (that too create on run time basis with the named as yesterday date). Means firstly Flow creates a folder with Yesterday Date & then save all the attachments of emails to that folder. It run on daily basis re-cursively.
This will save the flow run. As i have observed the scenario where user don't have subscription of much flow run. In that case this template would be very helpful.
Just an idea to make business process more efficient.