The best answer I could come up with is that EAS is a way to measure the equivalent dynamic pressure at SL hence it is the speed aerodynamically affecting the a/c (stall, handling, etc). I think this compressibility/density/pressure error has to do only with the calibration of the ASI (being set to only measure dynamic pressure correctly at SL ISA). So it's not actually a problem in the pitot tube with the air being compressed, (that would start being a problem above supersonic speeds I think..) but rather a miscalculation of the ASI because of the different ambient conditions than it is calibrated to measure speed in.
My conclusion: EAS is the way to mathematically correct the ASI for its error at different atmospherical conditions, giving us the ''true'' dynamic pressure affecting the a/c at all times!
Please reflect, I 'm just trying to find my way through!
