Do proponents of Free Software, on the whole, assert that the concept of intellectual property should not exist?
Are you referring to:
-copyright?
-patents?
-trademarks?
-something else?
Because, in general:
-copyright is obnoxious, but usable. The GPL depends on it.
-software patents are terrible, no excuses.
-trademarks are generally good and productive.
There is no one concept of "intellectual property," and most people using it are confused or being deceptive.
Copyleft licenses leverage the language of copyright laws to subvert the purpose of copyright laws: copyleft licenses roughly say you are authorized to do whatever you want to do with my content, as long as you let others also do whatever they want with my content.
> my content
So in other words, yes, proponents of "Free Software" do not, in fact, assert that that the concept of intellectual property should not exist.
We can imagine a society where copyright laws don't exist, i.e. content created by someone is not considered their property and others may do what they will with the content in a GPLisque manner. In that society we would never have to use 'my/their content', as there will be no notion of IP in that society.