Is this actually true? If someone said "the ability to use the black pieces to compensate for white's clear first-move advantage increases with skill level, so

Is this actually true? If someone said "the ability to use the black pieces to compensate for white's clear first-move advantage increases with skill level, so white's advantage is greater when the players' skill level is lower", I wouldn't find it any more or less convincing than your justification. Is there data we can look at?