In many cases where you need to brake/split several nodes it would be easier to have a right click menu which split/brake all selected nodes at once, instead of moving over with the pen tool and clicking on each node.
Erase Floating Nodes is essential where the “Remove Overlap” filter cannot be used.
I usually reconnect nodes again with the top + right node and bottom + left node.
Splitting or Braking several nodes NOT reconnecting (The requested function is not particularly needed for the case shown in uploaded image)
A similar function is available in Adobe Illustrator.
- But don’t you try to build a crossed path?
- did you try Path menu > Tidy up Paths?
Tidy-up paths pretty works as the concerned “deleting floating nodes”