The once common phenomenon of off-Broadway tryouts suggests very strongly the sacredness of the playwrights' words is grossly exaggerated. Shakespeare's words get changed or cut. Even when the would be playwright is kindly informed that his or her play is actually stageable, the stage director actually has a creative input into the acted play that the film director does not.
Great stage directors come and go, but the work of great playwrights lasts through the ages. The great plays are ultimately defined by their writers, not by the various directors who have staged them. And of course film directors have creative input in working with their cast, writers and the various departments involved in filmmaking.
I'm not sure why people keep talking about how some directors now also act as producers is even relevant to the thread.
The fact that so many directors attain producer status reflects how director-oriented the film industry is.
This stuff about how the director does this production task and that, as well as being the guy on the set who tells the crew ignores the fact that those decisions are determined first by the budget, which is not the directors' purview unless they are also producers. It is the guy who controls the money who ultimately decides whether a score doesn't fit, junks it and hires another composer. And so on and so forth. If the director is also producer, he has that creative input in his role as producer. It is secondary to the creative input from the screenwriter, but more important that his creative input as director. Directors who don't have such producer authority are dismissed as hired guns. Well, they are. Directors have been fired, lots of times.
Of course directors have to work within budgets. That's true of stage directors and film directors alike. That doesn't mean that the producer always has primary creative control in either medium, simply that directors have to achieve their creative goals within the economic limits set by the producer. And, as we've already discussed, there isn't a blanket rule that every film is director-driven. Some films are producer-driven and the director is just a hired gun, fulfilling a role more like that of a TV director. But in the case of major directors it's typically the director who oversees every creative aspect of filmmaking with the producer playing more of a logistical role.
The question of blame is the same as the question of credit. Giving the director credit is taking it away from the writer. If there's a script with words, he or she, not the director, is the primary creator.
If screenwriters could turn in their work and see it produced in the form they think works best then that outlook would make sense. But screenplays are generally the result of many rewrites, often by different writers (credited and un-credited), with the director and producer heavily involved in story meetings all the way through. The director is the constant guiding influence through pre-production, production and post-production.
Whether films would be stronger on average if writers were given more power to protect their work rather than working at the instruction of others is a separate question. The influence of directors on scripts will vary widely according to their talent and creative insight. Overall, giving greater respect to writers and allowing a single writer or writing team to craft a script with relatively limited input from others (or at least with input narrowed down to the director and producer) would I'm sure result in better films.
The fixation on who's more powerful ignores questions of creativity. That really isn't open to question: It starts with the writer.
The question of power is important to answering the OP's question in terms of who deserves the blame or credit if a film turns out well or turns out poorly. Blaming the screenwriter for a poor film hardly makes sense when the screenwriter doesn't have the power to write the screenplay he or she sees fit to write, but instead has to bend to the will of directors, producers, and studio executives. Similarly, when a film turns out well a good line or clever plot twist may have come from a director in a story meeting rather than from the writer, so assigning creative credit purely to the writer wouldn't make sense either.