Following on a discussion with Dmitry on IRC

Krita currently lacks an intuitive way to move selections. There's the global selection mask, but it can be slow and inconvenient on documents with a lot of layers (as it sits at the top of the layer stack).

Aseprite 1.2 beta 8 introduced a solution to move the selection: with a selection tool, click and drag on the selection's outline. Demo: http://imgur.com/yFPZOwx

It works that way, when the selection tool is active:
1. Drag inside the selection to transform it (there's no separate transform tool as in Krita that's aware of the selection)
2. If you drag on the selection's outline, you move the selection. 
3. If you click outside of the selection it creates a new one.
4. If you use a modifier key, you can still move the selection but not transform its content.

How it could work in Krita. With a selection tool active and selection in marching ants mode:
- Change the icon when you hover the selection's outline or content. The user clicks and drags to move the selection.
- If a modifier key is pressed, always draw a new selection.
- If you click once, as it works now, deselect everything
- if you draw outside the selection, create a new selection.

These suggestions take the overlay selection display mode in account. As there's not always a clear outline, you could interact the same way with both modes.

Anyway, it's up for discussion.