Generally speaking, I would think people would want their settings to move when they move the presets. From what I can tell, you have a specific case where you're only controlling an Axe-Fx, and you're doing the vast majority of programming on the Axe-Fx. You make changes on the Axe-Fx, then just need the preset names to change on the GT to line up with your Axe-Fx presets. But, anyone who controls multiple devices or makes more extensive use of what can be done in a preset would prefer that the presets move with all of their settings intact.
There are a couple of alternate solutions that would probably work better anyway:
1). Use "Get Preset Names" on the GT to read the new preset names from the Axe-Fx after you make changes.
OR
2). Go to the Devices tab, select the Axe-Fx device and click Set Preset PCs to Sequential. That will return the PCs in each preset to sequential order. You can do this after using drag and drop to reorder the preset list.
There are a couple of alternate solutions that would probably work better anyway:
1). Use "Get Preset Names" on the GT to read the new preset names from the Axe-Fx after you make changes.
OR
2). Go to the Devices tab, select the Axe-Fx device and click Set Preset PCs to Sequential. That will return the PCs in each preset to sequential order. You can do this after using drag and drop to reorder the preset list.