Using a national flag is a really bad UX pattern given the political ramifications and potentially offensive. Languages are not owned by countries. I am not aware of a multilingual site that provides over 200 languages in such a way that its country neutral (switching to a Spain based shopping site is not the same as switching to Spanish)?

As I've said before the mobile site doesn't remove it. It just changes the mechanism for understandable reasons based on the medium.

Nice to chat to you.