Some view shows “This field doesn't support this UI“ message as field value.

At some view, Jira doesn’t allow apps to render custom fields as the issue view. This issue depends on the Atlassian’s issue.

Can’t set default value.

The app can’t set field values without an issue because of security. So, default value can’t be set.

Can’t edit with bulk edit.

Bulk edit isn’t supported.
You may achieve your requirement with the Web API.

Can’t read value from workflow and automation.

The field value can be read by only the app, while the existence of the field value can be detected by anyone.

Can’t search values with JQL

JQL search is not supported because the field values can be read by only the app.

Does the app prohibit non-permitted users from all editing?

Non-permitted users can delete and alter value by special operation.

If users do illegal editing (except for deleting), the field show warning.

The editing will be logged in history activity tab. And you can use it as audit log.

Please inquire us if you have another question.