Is your feature request related to a problem? Please describe.
The problem right now is that it is difficult to drag a block in and out of a container type (Group, Columns etc) of block.
Especially in relation to activating the Top Toolbar.
https://github.com/WordPress/gutenberg/issues/21407#issuecomment-667944282
The up/down block move arrows only relates to the current level of the block that is selected. If one has selected the child block inside any container type of Block (Group, Columns, etc) the up/down arrows relate to the space inside the parent block.
Describe the solution you'd like
Let's make it possible to click the up/down arrows and move a block independent of the level it is at.
A wireframe example.
-- Group Block (parent)
--- Paragraph block 1 (child)
--- Paragraph block 2 (child)

Selecting Paragraph group block 2 and clicking the down arrow moves it out of the Group Block.
Using a snackbar notification?
Moving a block in/out of a container type block could show a snackbar notification letting the user know that they are now moving a block out of the current level it is at.
Reusable Blocks
Reusable blocks is a self contained block. One should not be able to move a block into it by clicking the up/down arrow in a block outside of it. Adding additional blocks to a reusable block can be done by clicking edit in the reusable block and then moving outside blocks into it.
Describe alternatives you've considered
Using the drag & drop to move blocks in and out of Group Block etc.
To me this seems a great idea. The only thing that pauses me is that maybe there are consequences — like for multi-column stuff – that I might not be foreseeing. For this reason I think that prototyping this would be necessary, just to make sure that something that seems a good logical idea doesn't have unintended consequences.
Two notes:
I don't think this should have a snackbar notification however. I think the behaviour is self-evident just looking at the screen.
I am bringing attention to this issue again as I noticed @afercia 's comment in the Accessibility slack channel:
"I mean: I was expecting the Move up and Move down buttons to move also across areas."
Actually the method I mention above could also be added to moving widgets between widget areas using the move up and down arrows.
@talldan @mapk @draganescu @adamziel
This can become a general feature in the post editor and in the widget screen.
We should also take care to announce via tooltip and aria labels that the block will leave its current nesting after the action is completed.
Here is an animated gif to show a visual of moving a paragraph block from inside the Group block and out of it.
As can be seen by noticing the breadcrumbs on the bottom.

I think it could be worth trying this. Some thoughts:
The first actionable item would be the issue I linked to just above. https://github.com/WordPress/gutenberg/issues/26020
In regards to be able to move widgets between widget areas using the up and down arrow icons.
The move arrow icons are used in many different situations. This also means that this would very likely not be a general feature but we should initially try it out with the blocks that need it the most. (After the above widget screen). What comes to mind is that we have for instance the Cover, Group and Columns blocks where moving blocks in and out of the container would create a helpful flexibility. As today it is tricky moving blocks in and out of these container blocks.
#26020 was closed as a duplicate. I think the widgets screen could be considered a use case of the proposed feature, but the implementation would likely be block editor wide functionality rather than specific to a single editor, so only this one issue is required.
Most helpful comment
To me this seems a great idea. The only thing that pauses me is that maybe there are consequences — like for multi-column stuff – that I might not be foreseeing. For this reason I think that prototyping this would be necessary, just to make sure that something that seems a good logical idea doesn't have unintended consequences.
Two notes:
I don't think this should have a snackbar notification however. I think the behaviour is self-evident just looking at the screen.