I haven't seen but but I wonder whether it's really difficult to act a wacky psychopath. You can do almost anything you like in the role and nobody can say you're getting it wrong or going over the top. Jack Nicholson and Heath Ledger both got high praise in their day.
I don't know if it's difficult or not to act so wacky, but it's clearly possible to do it wrong, and it's clearly possible to do it differently. Ledger, Nicholson and Phoenix all brought something totally different to the role, and Phoenix's performance and the story it's telling are truly remarkable.