@Krastanov While you can use just the rotation information and translation information to get the angular velocity, angular acceleration, translational velocity, and translational acceleration it is very limiting to require this.
Try and read through some of the mechanics documentation on Kane's method - it allows you to define generalized speeds in addition to generalized coordinates, to allow for very simple definitions of velocities which in turn have very simple accelerations.

ReferenceFrame works in a similar manner now (for angular velocities), in that if a user doesn't give an angular velocity vector, it is computed from the time-derivative of the direction cosine matrix. I think that's a good compromise between functionality supporting Kane's method and people wanting to use Lagrange's method and not supply that information.

I'm still trying to figure out if use cases that might break the position/translational workings - I'll report back when I'm done.