Your comment reminds me of the people who complain that a software author released some code under GPL, then produced a second project based on their own GPL'd code without releasing the source of the second project.
Actually, its quite possible for licenses (though probably not gratuitous licenses) to disallow this; a license can, for instance, by its terms be either completely exclusive or include some exclusionary provisions. In fact, such licenses are very important in quite a wide range of business scenarios.
No, it's not. Licenses do not restrict rights of the copyright holder, ever. They are a (conditional) usage license for people that are NOT the copyright holder.
EDIT: Yes, if the author is no longer the copyright holder, then this can occur - but this would certainly be a very strange and misleading way to describe that scenario.
Sure they can. You can definitely give someone an exclusive license, typically for a set period of time. You have agreed by contract not to license to anyone else, even though you are still the copyright holder. A license is simply a kind of contract, and you can contractually agree to whatever you want -- unless restricted by law otherwise, and there are certainly restrictions on legal contracts, but exclusive licenses are not at all unusual and entirely legal. Presumably you were compensated adequately for giving up (usually temporarily) the ability to license to anyone else.
Of course, open source styles of licenses including CC, are never exclusive, because this sort of license is offered to the public at large. When you CC-license, or GPL-license, or apache-license your work, you're are offering the work to the public at large under that license, that's what those kinds of licenses are for.
But traditional licenses are usually offered to a particular party, and they certainly can be exclusive.
An exclusive license is a transfer of those rights under copyright to which it is exclusive from the licensor to the licensee. So the licensee would be, for the rights in question, the copyright holder, even if they were not the creator and the holder of the remainder of rights under copyright (see 17 USC Sec. 101, 201).