I agree with you, even as a native English speaker.
I reside in Northern Europe where almost everyone speaks truly excellent English with a kind of formidable grammatical correctness. However, it is definitely spoken as a business/technical/lingua franca and not as a beautiful, poetic language in its own right.
I would love the people who speak it non-natively to truly own it by learning and caring about the nuances, idioms and poetry of English. Know and care for instance what it means when you have me in stitches, or he's a square peg in a round hole, or they got her goat or when someone sighs about a path not taken or says Ay, there's the rub.
English is as much about these idioms and aphorisms as it is about making grammatically correct declarative statements like "They write an email. I train an employee. It costs 17 euros. They respect the treaty. She prepares a speech."