User in my organization with Mobile Worker user type has requested me to give their privilege to work with 'Field Maps Designer'. When they log in, the landing page says 'You are not set up to create or edit maps. Ask ArcGIS administrator to change your privileges'.
ESRI technical support has clarified that Mobile Worker can not create web maps or apps in ArcGIS Online, they only have the ability to edit or modify existing data, such as collect data on their mobile device in a field maps project that has been shared with them. The Field Maps Designer's purpose is for the owner of the web map and content to set up smart forms and other functionality from the designer, so then the Mobile Worker can go out into the field and collect data.
If so, my suggestion is not to display 'Field Maps Designer' icon in Mobile Worker's login as it could cause conflicts between administrator and the mobile worker user.