This is absolutely not the case, angle of attack is not zero, but moreover most of the orbital insertion is exo-atmospheric and you can burn in whatever attitud

This is absolutely not the case, angle of attack is not zero, but moreover most of the orbital insertion is exo-atmospheric and you can burn in whatever attitude you want. The factor determining the accuracy of the apogee of your orbit is how accurately you can shut the engine off at the right moment and control your velocity.