@welovetraffic – Hmm that is the first time anyone has even mentioned that people might be trying via customizer to do this. And totally correct.
@bruno05, @hiddencrow09 – If you weren’t using the Customizer to edit the menu, and were in fact on the Appearance -> Menus screen, then it likely indicates another plugin or your theme has already added customizations to the menu editor in a way that is not compatible with other plugins doing so at the same time. In effect though, there is no real way we can overwrite that, as they are essentially doing it wrong.
Try the Health Check plugin’s Troubleshooting mode on our plugin. If it works while in Troubleshooting mode, then you know another plugin/theme is the culprit.
Hope that helps.