It's not. The nearside is also darker.

Earthshine is brighter than moonshine, sure. Earthshine at its brightest, delivers about 0.15W/sq meter to the moon. Sunshine meanwhile delivers 1360W/sq meter to the moon. The near side of the moon is the only side which experiences eclipses. The amount of energy from the sun is SO large, compared to earthshine, that ~1.5 eclipses per year for a few hours each represents a loss of light that outweighs the additional light gained from earthshine by about 5x.

We're talking fractions of a percent here of course, but it's not ambiguous. The near side of the moon is also the darker side.

You're right that it's noisier in radio.

Details for why ~40x: The Earth is 3.67 times larger in diameter in the lunar sky than the Moon appears in ours. Earth covers 13.5 times more visual sky area and is also about 3 times more reflective per unit area