I'm a first year assistant professor at an R1, and although I am overall quite happy, I've recently started down a small path of regret for skipping the post doc. At my institution, I'm expected to apply for grants, which I have zero experience with. I have also realized over the last few months that one of my weaknesses is in networking, which is important for both grants and collaborations. My mentor in graduate school became a full professor shortly after I started and didn't really attend any conferences with me throughout my graduate school career, which meant I wasn't introduced to people—I had to initiate contact on my own, which I rarely pursued. If I could just teach my courses, sit in my office and analyze data/write papers, mentor grad students and supervise clinicians, I'd be thrilled, but the job entails more than that. Had I done a post-doc, I would have been able to develop grant writing, networking and collaboration skills with my post-doc mentor and I likely would have been able to hit the ground running a little harder and faster than I am now, at least in the research domain.
On the other hand, I don't know that anyone feels "ready" for academia. There are days I sit in my office and think "I can't believe they are paying me to make my own schedule, teach however I want to teach and think about all kinds of fascinating psychological questions! AWESOME!" and there are other days when I think "They made a mistake; I have no idea what I'm doing or how to be a good faculty member."
I think it's possible to move up from an R2 to an R1 if you're willing to put in the work to get there. A postdoc might make it easier to land an R1 job up front, but as others have pointed out, there are advantages to taking the assistant prof route without a post-doc. I suppose some of it depends on how much faith you have in yourself to work toward your eventual goals and how much help you think you need to get there.