I get the choice of Joaquin Phoenix. He's someone I thought of as I read the question. I just find he's trying way too hard to come off like he's pushing boundaries. Once I watched James Dean in Giant, I saw the performance Phoenix has been trying to give naturally his entire career.
I knew there would be debate over the names mentioned, and whether or not they deserve to be called "great directors". It's missing the question by getting hung up on details. I was offering a general list of the type of actors considered great. So it doesn't assume any of them are good actors so much as make the case that every generation has their handful of great American actors.
To answer the question myself, I would say Leonardo DiCaprio, even though I wish he was still making the riskier indie fare he used to be drawn to. (I guess The Beach cured him of that.) Joseph Gordon-Levitt certainly has a couple of bold choices on his resume. Chloe Moretz is an inspired choice. Let's see if she can keep it up these next few years.
Woody Harrelson is also inspired, but I feel like he fits more as a character actor then as a leading man. But you're right, he's done some great work in unexpected films lately.
What about Philip Seymour Hoffman? Do you think he qualifies? And while it's easy to dismiss Brad Pitt as a Hollywood Movie Star, you have to admire him taking on films like Babel, Fight Club, Tree of Life and The Assassination of Jesse James by the Coward Robert Ford. Yeah, I think I'd have to change my answer from DiCaprio to Pitt.