On my last film I basically knew what I wanted, and hired an art director who just had to execute it ("ok, the chair should be some kind of funky wingback, preferably with a bright primary color like red or blue", "Those shelves should have board games, beat up ones from the thrift store", etc...).
That is what a director does with a production designer does, too.
Of course how a movie is made and what people are necessary
depends on hundreds of different things. But the director is always
in charge. At no time does having a production designer (or a DP
or an editor or a makeup artist or a costumer or....) reduce the
influence of the director. Specialists in their fields enhance the
directors vision and makes the overall production that much better.
The director knows what they want - the art department delivers.
On micro budget movies filmmakers cannot count on other people
to be skilled and experienced so often times the director feels they
must do everything. And most of the time the art department is
not even considered by filmmakers working with no money.
The bigger the project and the more ambitious the project the more
people are needed. Even really small projects can benefit from a
small art department. But only if the director/producer knows someone
who is dedicated.
Making a movie is damn complicated. Making one with good enough
quality to go to the film festivals and for DVD sales is even more
complicated. However, we all know of very small, very inexpensive
movies that have been in film festivals and have been sold on DVD.
That's what drives us, isn't it?