If you're moving your project to the FSF, it's because you want their lawyers to defend your users' rights under the GPL/LGPL/AGPL.
From the FSF[1]:
> Under US copyright law, which is the law under which most free software programs have historically been first published, there are very substantial procedural advantages to registration of copyright. And despite the broad right of distribution conveyed by the GPL, enforcement of copyright is generally not possible for distributors: only the copyright holder or someone having assignment of the copyright can enforce the license. If there are multiple authors of a copyrighted work, successful enforcement depends on having the cooperation of all authors.
> In order to make sure that all of our copyrights can meet the recordkeeping and other requirements of registration, and in order to be able to enforce the GPL most effectively, FSF requires that each author of code incorporated in FSF projects provide a copyright assignment, and, where appropriate, a disclaimer of any work-for-hire ownership claims by the programmer's employer. That way we can be sure that all the code in FSF projects is free code, whose freedom we can most effectively protect, and therefore on which other developers can completely rely.
tl;dr: the FSF can't enforce a project's license unless they're copyright holder.
From the FSF[1]:
> Under US copyright law, which is the law under which most free software programs have historically been first published, there are very substantial procedural advantages to registration of copyright. And despite the broad right of distribution conveyed by the GPL, enforcement of copyright is generally not possible for distributors: only the copyright holder or someone having assignment of the copyright can enforce the license. If there are multiple authors of a copyrighted work, successful enforcement depends on having the cooperation of all authors.
> In order to make sure that all of our copyrights can meet the recordkeeping and other requirements of registration, and in order to be able to enforce the GPL most effectively, FSF requires that each author of code incorporated in FSF projects provide a copyright assignment, and, where appropriate, a disclaimer of any work-for-hire ownership claims by the programmer's employer. That way we can be sure that all the code in FSF projects is free code, whose freedom we can most effectively protect, and therefore on which other developers can completely rely.
tl;dr: the FSF can't enforce a project's license unless they're copyright holder.
[1] https://www.gnu.org/licenses/why-assign.en.html