"Not all writers have that power."
Wrong.
According to the Dramatist Guild of America:
1. ARTISTIC INTEGRITY. No one (e.g., directors, actors, dramaturgs) can make changes, alterations, and/or omissions to your script - including the text, title, and stage directions - without your consent. This is called “script approval.”
2. APPROVAL OF PRODUCTION ELEMENTS. You have the right to approve the cast, director, and designers (and, for a musical, the choreographer, orchestrator, arranger, and musical director, as well), including their replacements. This is called “artistic approval.”
3. RIGHT TO BE PRESENT. You always have the right to attend casting, rehearsals, previews and performances.
So, yes, every writer, whether they be playwright, lyricist or composer, has those rights and can demand them whenever they see fit.
Theatre is not Hollywood. And thank God for that!
Dramatist's Bill of Rights
"Writing is like prostitution. First, you do it for love, then you do it for a few friends, and finally you do it for money." ~ Moliere