I think what ruins the sense of speed it is the camera. The third person camera is far out and way too fixated at the back. The track moves but the car feels very much fix. During first person the camera is relatively a lot more static too.
Some motion blur around the edges of the screen would have also helped
You can see this when you compare the three games. The car in PC and FM move a lot more on elevation and turns in 3rd person. There is more rotational freedom.The camera shakes in various angles to elevation and turns in first person too, but it is more subtle in GT. The camera is also closer to the windshield. You are not looking from the drivers eyes. Conveying the sense of G-forces help a lot in conveying speed which PC does better than Forza and GT in 1st person. You can see that the acceleration and speed pulls the camera backwards as it would have happened in rea life. The car in GT is affected by elevation and turns but since the camera is a lot more fixated it destroys the feel.of speed
Grid is completely unrealistic btw but the shaky camera and motion blur help