Your repeated use of “absolutely” in this thread is really misplaced, as your understanding of the 1st amendment is incorrect.
The 1st says that “Congress may make no laws…” respecting freedom of speech. That’s entirely different than some notion that the judiciary can’t enforce property rights or provide injunctive relief.
Are you familiar with the Streisand Effect? There are reasons to not sue that have nothing to do with whether a person was defamed or their likeness was misused.