However, many successful singers do sing with a neutral accent.  Many singers do sing in English with a neutral accent, which is otherwise known as a general American accent, because they believe this will increase the sales of their music to a larger American audience. 

Neutral accents are not mandatory for performers.  In fact, one of the successful actors is Mel Gibson who has used three different English accents throughout his highly successful career in the film industry.  He spoke in his native Australian accent during the early years of his career back in the 1980s, he spoke with a Scottish accent during his portrayal of William Wallace in the film Braveheart, and he has used an American accent in most of his other successful films.    

It's true that having different accents will give you more opprutunities!   Being versatile is probably a big bonus for an actor or actress.

But in the states, I feel like using the Standard American Dialect is very important.  That's how you hear Barack Obama speak or the way you hear most people speak on television.  In reality, there are hundreds of different accents in the US, but we only hear a fraction of that on TV.