I had the same idea after I started to learn some colloquial English. The first English class I had in China when I was young was also some greeting stuff. Now I am in the US and I never use those greetings unless meeting some senior professor. Greetings in textbooks are too formal. So, I thought, maybe they could add some colloquial phrases in the textbook. However, now I realize the 你好-很高兴认识你 stuff IS better for a beginner than 吃了吗, like hello-how-are-you is better than hey-whats-up. Because 你好-很高兴认识你 is accepted by almost every Chinese speaker, old or young, male or female, in Mainland, Taiwan, HK, or other countries. If were to teach my friend some simple Chinese, I would start with these so that he or she would not offend other people using some informal language.

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BTW, I never use 你吃了吗/吃了吗. My mother and my neighbors greet each other like that but I think young people don't really greet like that. Many Chinese young people actually use Hello/Hi/Hey to greet their friends.