The English phrase “Chosen people” was coined originally by anti-Semites, it’s never found directly in the Torah (Am HaNivchar, Goy HaNivchar, or something similar). They would use it to convince people to hate Jews “Look at these Jews! They think they’re so much better than us!”. Non-frum religious Jews reclaimed the term sometime after the European Churban to use it as a mark of pride.
So while I don’t disagree with these statements, I’m very leery of using the term in general to describe the Yidden.