Why is precession angular velocity constant?

I am currently studying precession, and have a question regarding the angular velocity of precession. Let’s simply use a spinning top in this case. I understand that it is given by the formula

$$
omega_P=frac{r Mg}{Iomega}, .
$$

The proof and derivation makes sense to me; however, I don’t quite understand the conceptual aspect of it. This formula gives that the angular velocity of precession is constant assuming no friction. It is clear to me that the torque is always perpendicular to the initial angular momentum vector so it moves the angular momentum vector in a circle. From this viewpoint, I can see that the angular momentum vector moves in a circle at a constant angular velocity around the z-axis.

However, shouldn’t this torque will also produce an angular acceleration of the center of mass of the top with respect to the z-axis? Thus, since the angular acceleration of the torque from gravity is in the same direction as the precession angular velocity, why does this not change the value of the angular velocity of precession?