“What I am saying is what is so wrong with simply saying “my son learns in Israel” or “I just cam back from a trip to Israel”?”
I think many people do use eretz Yisrael or Israel interchangeably, depending on the context. I do and so do most people I know.
I don’t know why it offends you if people like calling it that. People will title many things by terms that feel more right to them. For example, when some people refer to their mother they’ll say “my mom” whereas others will say “my mother”. Its just a matter of preference. One may be more grammatical but in casual conversation, neither is actually better or worse.