Is there any way to paint directly with the background colour?
By that I do not mean "swap foreground and background colours, then paint with foreground colour".
I've tried configuring RMB to Secondary Mode but it does nothing with the Freehand tool.

No, I don't think we've got anything like that.

Would there be any objections to me adding that functionality?

Nope, but we'd need to figure out how to make that usable, UX-wise. Would it be the property of a particular preset, for instance?