I think all other groups/orders have substantive reasons why they won't work in the general case.

When altering projects, tasks can have multiple projects. Does dragging from "X" to "Y" mean "remove all projects and replace them with Y", or "remove X and replace it with Y", or "add Y"? I'd worry that picking any of those answers would sometimes leave the interaction confusing.

Priority has the nice property that the whole list is ordered (we maintain a hidden "subprioirty" to distinguish between two "High" priority tasks). If you have a view like "Group by status, order by date created", and drag a "Closed" task up a few slots but don't drag it out of the "Closed" group, the operation is meaningless.

When viewing large selective lists of tasks, the thing you'd like to drag a task into (e.g., an assignee or status) may not be present in the list (or may be on a separate page), making the operation impossible.

Generally, this UI just isn't a good one for most of these operations.

In the future, we do plan to implement column logic on boards (so, e.g., you could close a task by dragging it to a "Done" column). There are also more opportunities to make interactions easier there (e.g., we can reasonably guess who you might want to assign a task to based on project members, and could provide quick ways to assign things).

In some cases, you might also want to try using the batch editor. For example, this can be useful when triaging tasks -- suppose there are 20 new tasks, and you realize 8 of them should be in the same project. You can shift-click the tasks you want to change, then "Batch Edit Selected", and add the project. This isn't the most elegant interaction, but it's a bit better than doing 8 separate edits, at least.