Is there any way to clear routing in an area without removing placed components?
Yes.
Go to the OpenGL/Cairo canvas.
Hide the components by unchecking top and bottom components from the Visibility panel.
Eventually hide the silkscreen or other layer that you may have used.
With a rectangular selection you can now select all the tracks and vias in the region of interest.
Then delete the selection 
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And for the 3rd canvas option… in default canvas, when you make a selection rectangle it will ask you what you want to deal with… just deselect the footprints and do what you need to do…
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Is this really true?
I find it wants to select things regardless if layer is turned off.
It drags wires, selects parts etc.
Disregards what is visible or not.
Cairo
4.0.2+ windows 7, 64
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You want to delete wires, so this is good, right?
Are you sure that you unchecked “Footprints front” and “Footprints back”?
This is different from “Pads front” and “Pads back”.
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But when you drag wires on top layer you don’t want it to select wires on layers that are turned off.
The other thing you mention I am sure I have not tried, beacuse thus is first time I hear about it.
Will try.
Other tools hace component check boxes.
Turn of top / bottom.
Saves you toggling:
1 pads
2 fab layer
3 silk screen
4 court yard.
Everything related to the component / footprint gets turned of in a single click.
Would be nice to have in kicad also.
BTW
This habit of selecting hidden things also is the same in footprint editor ( Cairo)
BTW 2
Another big problem when you try to do a drag select and happens to hit a locked component when you “put down the start cursor”
He snaps out of the select and starts talking about the locked component instead of waiting for the select to be completed and then realize that the locked component was not entirely within the select region and thus was not about to be selected anyway.