There are no global component configs for com_tags, similar to com_categories.
The only "global" setting is coming from the "System - Fields" plugins. There you can specify the default appearance for the fields.

there is just one Option below the "Integration" Tab for enabling Custom Fields or not...

That one is actually an option from com_content.

If we want to add global options to the com_fields component, it means we have to rewrite the component a bit so it can work standalone (eg it needs a menu item and you can switch between extensions from within it).
As it is now it tries to blend in with the "parent" extension (eg com_content). Similar to com_categories.

So it's basically an UX question in the end. Technically, it's possible to change it.

Either we would have to remove the Options there then or solve it like you propose... I´d prefer the second to have consistency in the CMS.

I think this proposal would more confuse people. You are also not able to enable the images fields of an article for specific modules or menu items.

Either we would have to remove the Options there then or solve it like you propose... I´d prefer the second to have consistency in the CMS.

Actually, the current state is consistent with how it is done for categories. They are done by com_categories but the options button goes to the respective extension (eg com_content).

As Allon said, you would not be able to say where fields should appear (eg not in modules). Com_fields doesn't have any knowledge about that.
That's the job of setting up the fields correctly and having the right overrides in place.

Set to "closed" on behalf of @franz-wohlkoenig by The JTracker Application at issues.joomla.org/joomla-cms/13700

closed as Expected Behaviour.