You're conflating the right of control of exploitation with copyright, which is a legal creation to protect that right.
The two are close, but not synonymous. Take photographs: the exclusive first-use of a photograph is a big thing. If you publish my picture without my permission, my right of control is gone.
I can use copyright laws and the courts to try and get economic redress for that, but nonetheless I no longer have the ability to decide where and when that picture is first published; the ability was stolen from me.
Yes, I assumed you were speaking of copyright. Copyright gives you a monopoly on your work. Is this what you mean by the "right of control of exploitation?" Is there another law that gives that right or are you speaking from a moral standpoint?
Copyright doesn't prevent copying, it just gives you a way of redress.
UN Declaration of Human Rights (ratification varies by country; your mileage may vary) enshrines a right to control of the exploitation of your works, yes.
You could sue for everyone for copyright infringement. (This didn't work so well for the RIAA.)
Or you can figure out a way to capitalize off the reason why everyone likes your work.
In any instance you don't lose your copyright.