If only conservative forces were involved, the amount of energy required to get the car to 60 mph is the kinetic energy of the car at 60 mph (0.5*m*v^2), regardless of how you got to 60 mph, i.e. fast or slow acceleration. But there are non-conservative forces involved in propelling a car. Hence it makes a difference how you get from point A to point B, i.e. how you accelerate.
As an example, suppose I accelerate slowly so at the end of 1/4 mile I am going 40 mph. Alternatively, I could accelerate quickly getting up to 40 mph and then maintain speed to finish out the 1/4 mile trip. I am able to make accurate measurements of energy usage with my car (non-Tesla). In the first case, I measure the total energy required to be 0.120 kWh. In the second case, it is 0.148 kWh. Much of the difference results from the additional friction due to higher average speed for the second case. That accounts for 0.01 kWh of the difference. The remainder of the difference, 0.018 kWh, is mainly due to motor efficiency effects. The motor operates more efficiently during acceleration. With slow acceleration, you are accelerating longer and the motor is operating more efficiently longer. The remainder is due to less efficient transmission of power from the motor to the road during fast acceleration.
As an example, suppose I accelerate slowly so at the end of 1/4 mile I am going 40 mph. Alternatively, I could accelerate quickly getting up to 40 mph and then maintain speed to finish out the 1/4 mile trip. I am able to make accurate measurements of energy usage with my car (non-Tesla). In the first case, I measure the total energy required to be 0.120 kWh. In the second case, it is 0.148 kWh. Much of the difference results from the additional friction due to higher average speed for the second case. That accounts for 0.01 kWh of the difference. The remainder of the difference, 0.018 kWh, is mainly due to motor efficiency effects. The motor operates more efficiently during acceleration. With slow acceleration, you are accelerating longer and the motor is operating more efficiently longer. The remainder is due to less efficient transmission of power from the motor to the road during fast acceleration.