It is human nature to want to integrate into groups. Sounding like a native helps you do that.

I am not a native English speaker but people sometimes do not notice that. I appreciate that, it makes me feel that I mastered something I wasn't born around. 

But you know, having an accent can sometimes be a good thing. People consider it funny, cute and even sexy. 

Some students may think that acquiring a native accent is a short-cut to fluency.

In my experience, some students like the idea of sounding like a native speaker, but then quickly find the reality of sounding very different from their usual accent a bit disturbing. 

I feel that when people talk about losing their accents they really mean improving their pronunciation. I've heard people with accents that have perfect pronunciation but still have that accent. It doesn't affect their pronunciation, per se. There's this extra yawn or space in their mouth. I don't know it's a bit esoteric. When you hear it you just know. 

In any case, I'd tell those people to focus more on their pronunciation and less on their accent. If you're understood clearly, that's what matters. But then comes the issue of Australians, Scottish people, or Appalachian people who I have hard time understanding sometimes. Then "accents" become a matter of politics... 

I guess the general "American" accent is the most neutral one, and if you speak in that accent you'll be understood by most people. I think the end goal is to sound more like the people you hear all the time. Which makes sense, however I think this can only be conquered through time and patience. The more you speak, the more you hear, the more natural the language will feel to your tongue and ears.

Also, I think you could get away with accents in languages like English, but imagine that in Chinese? Being a tonal language that would probably screw you over more than a couple of times.

Honestly, this isn't something that I would worry about unduly.

After all, communication is king and an accent is only ever a problem if it prevents you from being clearly and effortlessly understood.

The reason I have mentioned "effortlessly," as well as 'clearly,' is that, in a social context, people do not generally want to have to work hard to understand somebody.  So if your accent is such that you can only be understood by somebody listening very closely to you, that may inhibit you in social situations.

Funnily enough, one of the areas where I suspect non-native speakers are most keen to acquire a 'native,' accent is actually in the area of English language teaching.  Non-native English teachers sometimes face prejudice on account of not being native, so "getting rid," of the accent that comes from their mother-tongue is one way to perhaps diminish any prejudice.