The constant-pressure method can give good results if used with extreme care, but there are some things that influence its accuracy:
(1) Calibration values change constantly during a ride, as portions of the course may be in hot sun, while others may be shaded. If the pressure in the tire is adjusted to match that of the precalibration, it may be necessary to be sure that the conditions are the same.
(2) While it may be possible to measure, say, a 5 km course in 20 minutes, and while the pressure may stay relatively constant during that time, it is more common for a 5 km measurement to take a few hours, as it rarely comes out right the first time, and requires adjustment. During this time the pressure is going to change. What is to be done? Take a reading every half hour, and release air or pump it in to maintain a constant pressure? This is risky business.
(3) If the tire pressure is not adjusted during the measurement, but is checked afterward, it will be found to be different than at the start. What is to be done with this information? If my tire pressure is 125 at the start and 122 at the end, what do I do about it?
Given the above I can see no reason why the pressure method is in any way easier or better than the method we use now. The fact that it can be used by a knowledgeable individual with custom pressure-measurement equipment does not make it a better method. The precal-measure-postcal method frees the measurer from any concern about his tire pressure and allows him to focus on the measurement itself. This makes mistakes less likely.
As the sole benefit of the pressure method is to avoid postcalibration I believe the cure is worse than the disease.