Whether you need a warm-up or not seems to be a personal issue, and there seems to be a lot of opinion out there. I believe there is anecdotal evidence that suggest there is a physiologic benefit to warming up your embouchure muscles. As Rowuk has suggested elsewhere, there may also be a psychological benefit to warming up as well.
I play slightly off-center, to the right. I point the horn slightly downward. I believe this is because of variation in the alignment of my teeth and natural position of my jaw. I don't believe it causes any limitations. I believe forcing myself to play dead center would have limitations.