This is just incorrect. By default, you retain the copyright to things that you write. Which means that others can't make copies without getting your approval. And in many jurisdictions, it is not at all clear that you can relinquish your copyright simply by declaring your work to be in the public domain. So by default, there are legal restrictions on what others can do with things you write.

It's called a "license" because it enumerates the things you are explicitly _allowing_ others to do with something you hold the copyright to. Without a license, the default "rules" of copyright apply. Licenses don't impose restrictions, they remove them.

Liberal licenses (BSD, MIT, etc) allow you to do nearly everything you can do with something in the public domain. Copyleft licenses (GPL, etc) allow you to do somewhat less, with the notion being that this restriction of your freedom increases the overall freedom of everyone.

Actually the restrictions are imposed by copyright law. A license is used to lift away these restrictions.

I would agree about public domain, if it existed everywhere in a usable manner.