Why is the cinemachine spline dolly controller so terrible?

The spline path is intended to control the position only, not the rotation. Don’t try to use the rotation of the knots, it will fail miserably.

Cinemachine 3.1.1 comes with a component to do exactly what you describe: make the camera look at specific things at specific points along the spline. See the description here: Cinemachine 3.1.1 is Now Available