Power required = Drag x TAS
So to fly with a 60 knot TAS you would need what you have described as "60 knots of power".
But before you start the takeoff run, when standing on the runway in the 50 knot headwind you would already have 50 knots of TAS. Assuming that you had zero friction wheels and axles you would need to generating sufficient thrust and to stop you from being blown rearwards.
But because you already have 50 knots of TAS you only need 10 knots of acceleration to reach the 60 knot take-off speed. It is this reduced acceleration requirement that reduces the take-off run.
At the point of take-off the TAS would be 60 knots and the GS would be 10 knots. If by some magical trick (or Star Treck-type transporter system) the ground were to be suddenly removed, the TAS would still be 60 knots. The aircraft would still be flying, and it would need what you have descsribed as "60 knots of power" to continue flying.
As I have said earlier your statement that "aircraft in flight do not experience the wind", is untrue or at best misleading.
It would be more accurate to say that an aircraft in flight cannot distinguish between airflow due to the wind and airflow due to movement of the aircraft. From the point of view of the aircraft and the ASI it is all just airflow. But even this is untrue of modern aircraft with inertial navigation or GPS systems and Flight Management Systems. In these aircraft the inertial velocities are compared with the airspeed velocities to determine the wind speed. But that sort of stuff is for your future studies!