You might be in luck. While I can’t say why Marx didn’t mention the reasons why he didn’t do that,

He did mention why U.S wage laborer earned relative higher, compared to their British and European counterparts, in Chapter 33 of Capital

We have seen that the expropriation of the mass of the people from the soil forms the basis of the capitalist mode of production. The essence of a free {settler} colony, on the contrary, consists in this — that the bulk of the {indigenous}soil is still public property, and every settler on it therefore can turn part of it into his private property and individual means of production, without hindering the later settlers in the same operation.[10] This is the secret both of the prosperity of the colonies and of their inveterate vice — opposition to the establishment of capital. “Where land is very cheap and all men are free, where every one who so pleases can easily obtain a piece of land for himself, not only is labour very dear, as respects the labourer’s share of the produce, but the difficulty is to obtain combined labour at any price.” [11]

In other words, in a world of Euro-Amerikan petty bourgeoisie settler proprietors, why be a wage laborer? Hence, to attract more wage laborers, a transitional above-average wage was put into place, by necessity.

Only when

the expropriation of the mass of the people from the soil

by growing Capital is in major process, will Capital thus reduce and later equalize the wage of wage laborers to what it is in Europe