This is wonderful. You really put a lot of thinking in it. It's amazing that you summarize so much. I never thought about these. As a result, I agree with your ending the most. I think most people are speaking "funny" English not because of their accents, but because they used the wrong words/expressions. It will be even funnier to speak in a native accent but using funny experssions. I still believe English is beautiful because of all the accents, because it re-invent itself all the time.
Other factor is the setting. Street people tends to be more impatient with foreign accents however the vocabulary is not big. In professional or academic setting, people tend to be more understanding.