Yes, but not so much budget as screen time.
I'm not an authority on this by any means--this is just a theory. But it seems to me that the director got fixated on plot. This is what a good director should do if they want to tell a story *and* make money. I don't think he hacked the plot in order to save money on actors. I think he decided that _no_ actor could adequately portray the depth of Theoden (a secondary character) and Faramir (also a secondary character) in the sum-total of five minutes screen time alloted to them. Doing so would haven taken more film, which would have detracted from the primary characters and plot. In other words, plot* drove character which drove the "look" which drove the budget, not the other way around.
But that's just a theory.
* by "plot" here I mean specifically the drive among big-screen directors to keep the story simple and focus on primary characters. This is such a truism in Hollywood (and imitators of Hollywood) that it's often not discussed, and so is overlooked by people outside that subculture.
