Hi Jay, agreed this would be useful!
I just tried and seem to be unable to do this. I expected to be able to disable the "Locate" feature in Desktop, but keep it enabled in the Mobile version if the inheritance setting was Custom. But the setting seems to apply at the Map level and to both formats regardless.
Sorry. Hopefully someone else has a workaround!
Only the size and position settings of a widget can be changed for different sized devices. Generally speaking, settings in the "Content" panel will always be applied on all sized devices.
It is my understanding that the only way to do what you are asking would be:
1. In the view for small devices, duplicate the Map Widget (called, for example, Map2).
2. In the view for small devices, move the original Map Widget (called, for example, Map1) to the pending list. This is primarily what the pending list is for - hiding widgets for the device size you are working on configuring.
3. Set the Locate Tool as desired on Map1 and Map2.
The pending list can get long in larger projects making things a bit complicated.
I couldn't say how it affects performance. I haven't tried anything to see if it does. Here is the conversation I had with @DanJiang about using the pending list: https://community.esri.com/t5/arcgis-experience-builder/limitations-of-refining-layout-for-all-devic...
Perhaps @DanJiang will answer your question about whether or not we should be concerned with performance issues.