Is there even actually a default license for public projects? I couldn't find anything except that if you have a public project you permit people to fork it.
Mandating a license (any license) but perhaps offering a selection to be automatically included would be a really good idea.
I wonder if you could actually put a license that gave permission to fork/clone but not actually to run/distribute outside github or otherwise use the code or derivatives thereof. I've not tried and wouldn't try to go against the spirit of Github in that way but it seems as if it might be permissible.