Hell, yes.
A very few non-native speakers speak English so well, that they are indistinguishable from native speakers. They are usually Dutch, or speakers of another Germanic language. Some accents are wonderfully charming. At the other end of the spectrum, a mangled accent can render a person's “English” completely incomprehensible. (Would you have known that “fly lie” was “fried rice”?).
Achieving an an accent that, at least, does not put a strain on the ear, is for the benefit of the non-native speaker. Whilst you may be able to communicate, you have no idea of the real reaction of your conversation partner. As for conversing with other non-native speakers, you can probably communicate with them more easily than with native speakers. However, you may not notice it, but good non-native speakers of English will probably have a similar reaction to you as native speakers. This means that the non-native speakers you feel comfortable communicating with do not speak well either.
Life is unfair. English is the international language and native speakers of related languages have an advantage when learning it. Then, there are the French. (Don't get me wrong, I speak French and love it, but they do tend to have a horrible accent in English.) Oh, and the Japanese. If you wish to torture a Japanese person get them to say “Ralph Lauren” a few times. Definitely unfair.
A very few non-native speakers speak English so well, that they are indistinguishable from native speakers. They are usually Dutch, or speakers of another Germanic language. Some accents are wonderfully charming. At the other end of the spectrum, a mangled accent can render a person's “English” completely incomprehensible. (Would you have known that “fly lie” was “fried rice”?).
Achieving an an accent that, at least, does not put a strain on the ear, is for the benefit of the non-native speaker. Whilst you may be able to communicate, you have no idea of the real reaction of your conversation partner. As for conversing with other non-native speakers, you can probably communicate with them more easily than with native speakers. However, you may not notice it, but good non-native speakers of English will probably have a similar reaction to you as native speakers. This means that the non-native speakers you feel comfortable communicating with do not speak well either.
Life is unfair. English is the international language and native speakers of related languages have an advantage when learning it. Then, there are the French. (Don't get me wrong, I speak French and love it, but they do tend to have a horrible accent in English.) Oh, and the Japanese. If you wish to torture a Japanese person get them to say “Ralph Lauren” a few times. Definitely unfair.