It should be possible on an SFM to configure that this runs automatically on a Load, Save or Both just like you can with formulas.
Currently it does not run automatically and you will have to manually click the search icon for it to trigger and fill the fields. This would make the Form Fill extremely powerful to use as it can get values from records related to other objects not configured as an object in the SFM transaction. This includes objects that could not possibly be configured in the SFM transaction and a formula can then never be used.
With this we can prevent the usage of formula fields, process builders, flows, apex code to get the fields populated.
Scenario, we create a Work Order from a Case. Both the Case and the Work Order to be created is linked to an Installed Product and it's Installed Product Location (Site). Because we create the Work Order from the Case it is not possible to add Location to the Work Order. And when the Work Order is created we want it to automatically fetch information from the Location like the Longitude/Latitude/Address Fields. We might even want to map values from the Installed Product record also like Firmware Version, Software Version, Serial Numbers etc.
Form Fill can already do this, all it needs is the option to have it run on a Load or Save.
What is the underlying problem do you intend to solve with this idea?
Effectively retrieve information without additional configuration outside the SFM
How is the problem being addressed today, if at all?