Timezone with ISO date format

While reading the documentation I don't see anywhere that a date in the ISO format shouldn't be able to select a custom timezone i.e. a timezone attached to the date.

Yet I see the timezone drop down list only when I create a field of "Date" format and I've reflexively always chosen Date when setting up a new project and I've needed a timezone.

When I create a field of "Date (ISO)" format, no timezone drop down list appears. I've inherited a site that has used the Date (ISO) format — and now we'd like to set the timezone for them without copying the data into a new field, if possible.

When describing each date type, should the documentation say, "Use the Date type when you want to set the timezone for the date via the UI; Date (ISO) cannot set timezones via the UI."

-André