Location switcher not working on mobile

I have an issue with the location switcher not working on mobile devices. Researching the forum I understood that the ajax loaded form doesn’t work on mobile, but the visitor has to type in the city in the search city field. Is that the case?

This is too bad, since I think it’s unlikely the visitor will type the city, he probably will think that the only cities available are the few that are shown in the dropdown.

I read a comment about enabling “Show all locations in dropdown”. This would work for me, since I only have 14 cities. But ticking that option only shows all locations in a dropdown on the add listing form, not in the main menu. Is there any way of having the location switcher in the main menu show all the locations as well? I would prefer this even for the desktop site.