city, state, zip code only?

If the listing type is using the physical address setting, then all the fields are required.

However, the street component can be any old thing, and doesn’t need to be accurate.

If your directory will work by city, what you can do is:

Ask users to choose a location/city where they provide service, and then advise them in the description field help text to enter something nearby. You can change that text in the field settings.

To serve your listing owners, you can merge small towns into the bigger cities so all the listings show up in the same city.

Use the bulk actions on the cities tab to merge cities:
https://wpgeodirectory.com/docs-v2/addons/location-manager/#cities