accelerations map directly to actions of the user (forces). It seems fairly natural, not strange, to control velocities and positions in terms of accelerations. The same thing happens in real life.
applying a force perpendicular to the velocity does not change the speed, only the direction. Only the component of the force tangent to the velocity vector (the projection) is relevant for controlling the max speed
They're not measuring the projection of the acceleration vector on the velocity vector, they're measuring the projection of the velocity vector on the acceleration vector and limiting that. Which makes no sense for a speed limiting method as evidenced by the fact that strafejumping exists. What you said is true and also irrelevant.
To get a true speed limit you would compute the new velocity vector, compute its magnitude and rescale the components by the ratio under the limit. Which is slightly more computationally expensive I suppose.