It would be nice to be able to drag & drop grouped cards, so their status values are changed accordingly.
Example: https://coda.io/t/Super-Simple-To-do-list_tvg70LiomCg
In this example drag&drop can only be used to sort the todos, but it seems you cannot drag and drop a card to change the “grouped by” field (in this case ‘status’).
I have a setup where cards can be dragged between grouped fields.
How so? Does it need tweaking with automation, maybe? 
To make sure we are on the same page (i.e. talking about the same thing) I created the following:
When I drag and drop the Fishing task to Done, it works:
I can share the document if it helps.
Hi, would be great if you can share, so I can have a look. I’ll send you my account as a message.
Actually made a shareable version. You can make a copy to edit and play around with it:
https://drive.google.com/file/d/1_YJChFoWWbO012GP32BIPvCjZOjWOkgj/view?usp=sharing
