I don't know where you got the idea of "under US influence", but mixed Korean/Chinese character writing was common in South Korea well into 1980s, long after Korea became its own country. For example, in 1987, the newly founded Hankyoreh newspaper made a splash by deliberately writing all articles in pure Korean script, which was not the norm until then.
Gradually more books and newspapers followed suit, because pretty much everybody found that writing everything in Korean letters actually make communication less ambiguous and easier to understand. If your phrase is ambiguous between whether someone's offering apples or apologies, then you just change the word or add additional context to make it clear which one is being offered. It's no different from how English speakers deal with bear/bear, tear/tear, arm/arm, ground/ground, and so on.
Gradually more books and newspapers followed suit, because pretty much everybody found that writing everything in Korean letters actually make communication less ambiguous and easier to understand. If your phrase is ambiguous between whether someone's offering apples or apologies, then you just change the word or add additional context to make it clear which one is being offered. It's no different from how English speakers deal with bear/bear, tear/tear, arm/arm, ground/ground, and so on.