Your question already contains the answer. As you say

kinetic energy is proportional to velocity squared, so it is easier to accelerate air from 0 to 100 m/s than from 100 to 200 m/s.

The same is true for the air flowing through the propeller disk. Even if we replace the propeller by a black box, or better a black disk, which simply adds a bit of pressure to the air flowing through it, accelerating air from 0 m/s to 10 m/s is much easier than accelerating it from 100 m/s to 110 m/s. Since engine power is constant, the absolute speed increase will be smaller the higher the entry speed becomes. Thrust is the difference between the impulse of the air flowing towards the propeller disk and the impulse of the air exiting it, so a smaller speed increase means less thrust at higher speed.

The exit speed increase in turbojets is much larger so this effect becomes much smaller in jets. Also, jets benefit from higher entry speed by precompressing the flow ahead of the intake, an effect which raises mass flow through the engine and increases thrust with the square of airspeed. In the subsonic realm both effects roughly cancel each other, so thrust is approximately constant.

Your question already contains the answer. As you say

kinetic energy is proportional to velocity squared, so it is easier to accelerate air from 0 to 100 m/s than from 100 to 200 m/s.

The same is true for the air flowing through the propeller disk. Even if we replace the propeller by a black box, or better a black disk, which simply adds a bit of pressure to the air flowing through it, accelerating air from 0 m/s to 10 m/s is much easier than accelerating it from 100 m/s to 110 m/s. Since engine power is constant, the absolute speed increase will be smaller the higher the entry speed becomes. Thrust is the difference between the impulse of the air flowing towards the propeller disk and the impulse of the air exiting it, so a smaller speed increase means less thrust at higher speed.

The exit speed increase in turbojets is much larger so this effect becomes much smaller in jets. Also, jets benefit from higher entry speed by precompressing the flow ahead of the intake, an effect which raises mass flow through the engine and increases thrust with the square of airspeed. In the subsonic realm both effects roughly cancel each other, so thrust is approximately constant.

Your question already contains the answer. As you say

kinetic energy is proportional to velocity squared, so it is easier to accelerate air from 0 to 100 m/s than from 100 to 200 m/s.

The same is true for the air flowing through the propeller disc. Even if we replace the propeller by a black box, or better a black disc, which simply adds a bit of pressure to the air flowing through it, accelerating air from 0 m/s to 10 m/s is much easier than accelerating it from 100 m/s to 110 m/s. Since engine power is constant, the absolute speed increase will be smaller the higher the entry speed becomes. Thrust is the difference between the impulse of the air flowing towards the propeller disc and the impulse of the air exiting the propeller disc, so a smaller speed increase means less thrust at higher speed.

The exit speed increase in turbojets is much larger so this effect becomes much smaller in jets. Also, jets benefit from higher entry speed by precompressing the flow ahead of the intake, an effect which raises mass flow through the engine and increases thrust with the square of airspeed. In the subsonic realm both effects roughly cancel each other so thrust is approximately constant.

Your question already contains the answer. As you say

kinetic energy is proportional to velocity squared, so it is easier to accelerate air from 0 to 100 m/s than from 100 to 200 m/s.

The same is true for the air flowing through the propeller disk. Even if we replace the propeller by a black box, or better a black disk, which simply adds a bit of pressure to the air flowing through it, accelerating air from 0 m/s to 10 m/s is much easier than accelerating it from 100 m/s to 110 m/s. Since engine power is constant, the absolute speed increase will be smaller the higher the entry speed becomes. Thrust is the difference between the impulse of the air flowing towards the propeller disk and the impulse of the air exiting it, so a smaller speed increase means less thrust at higher speed.

The exit speed increase in turbojets is much larger so this effect becomes much smaller in jets. Also, jets benefit from higher entry speed by precompressing the flow ahead of the intake, an effect which raises mass flow through the engine and increases thrust with the square of airspeed. In the subsonic realm both effects roughly cancel each other, so thrust is approximately constant.