Yes, more proficient people will have higher standards of living than less proficient people. That obvious fact is not what the law of association is about. It shows that both the more proficient and the less proficient have higher standards of living by specializing in their areas of efficiency and trading with each other instead of remaining in self-sufficiency.
The law means nothing more and nothing less for groups of people. If people in one country are less proficient than those in another country, then their wages will be lower. The lower wages will attract capitalists and entrepreneurs who can gain by investing their production processes in the low wage areas. This process continues until there is no differential advantage for capital investment to move from one area to another. This is the process that was underway in colonial America and brought American wages from subsistence up to British standards in a century. This process has been underway in China for several decades, raising the standards of living of hundreds of millions of people there.
As long as the market is allowed to function, differences in the productivity of different factors of production will generate differences in their prices which will generate profitable arbitrage possibilities. By exploiting these opportunities by rearranging production, entrepreneurs and capitalists raise standards of living.