I wouldn't say it's a point of pride in the US usually, because it does make life difficult and limited. In the US, a lot of situations simply require English. It means relying on friends and family as translators, so the person can be at their mercy. They also can become very isolated within their immigrant communities while they watch the younger multilingual generations be able to integrate. My impression is that it is usually older people who struggle most learning English that remain in this group. I can't think of anyone who is even vaguely younger who didn't make an effort to learn English.

I remember a middle aged Iranian woman who was taking ELL courses at my university. We happen to be at the gym at the same time some nights. I could tell it was a struggle, but she was clearly picking up more of the language.