MS List saved to a Sharepoint Site Vs to 'My Lists' and Managed Metadata Column

Hi

I am trying to understand the new MS lists behavior

When I create a list and save it to a Sharepoint site , I am able to add a managed metadata column to the list/ however, when I save a new list to "my lists" it does not have the managed metadata column option

Can someone explain this behavior? it there a way to gain access to the term store even when my list is not connected to a site? 

Thanks

Gali