[...] assuming zero position and instrument error, the airspeed indicator is showing us EAS even in "high"-speed environment (M > 0.4)?
The ASI reading, neglecting imperfections, only agrees with EAS when the ambient pressure and density are at the ISA MSL values.
[...] airspeed indicators get dynamic pressure by substracting static pressure (static port) from total pressure (pitot tube).
This is not true. The indicator uses something other than dynamic pressure. There are a number of available solutions to Euler's equation of which only one is the (incompressible) Bernoulli equation. The (incompressible) Bernoulli equation imposes the condition that density must be held constant along a streamline. While this condition will not be observed in a real physical process, the Bernoulli solution is still adequate until roughly Mach 0.3. Nevertheless, modern airspeed indicators are not designed to make use of the (incompressible) Bernoulli equation.
Among the several other available solutions to Euler's equation is one which has been variously described in the literature as the Saint-Venant equation, or the compressible Bernoulli equation, or airspeed indicator calibration law. This solution does take account of the variation in density along a streamline and is valid up to and including Mach 1. An extended version of the solution, called the Rayleigh Supersonic Pitot equation, exists for > Mach 1, valid up to roughly Mach 3 or 4. A further solution exists for the low hypersonic regime taking account of quantum mechanical effects once vibrational modes become excited. And so forth.
A problem arises if the term "dynamic pressure" is intended to refer to the difference between static and total pressures because the total pressure predicted depends on which solution to Euler's equation is chosen. NACA addressed the nomenclature on this point in the 1940s (
c.f. aforementioned report) by introducing the term "impact pressure" (symbol: q_c) to mean the difference between the pressures with the total pressure determined by considering an isentropic process to account for density variation along a streamline. Some authors refer to "impact pressure" as "compressible dynamic pressure." In summary, airspeed indicators make use of neither the (incompressible) Bernoulli equation nor dynamic pressure.
"The ASI is calibrated to the ideal incompressible flow formula. Because of this a subtractive compressibility factor correction has to be applied"
Which textbook states this?