An English speaker with good accent is likely to get hired in the first place and get more promotions than others. The image it builds in public places makes you feel confident and presentable.
No doubt vocabulary and grammar are important for good English, but to be accepted as a good orator proper speaking skills like voice & accent training and pronunciation are crucial. Here the importance of neutral accent cannot be overlooked.
Many people speak English with good vocabulary but they lack in pronunciation skills.
The main advantage of correct pronunciation skill is that it makes you feel confident and comfortable. It helps avoid saying ‘sorry can you repeat that’ sentences. And well, honestly, I would recommend even teachers to pursue this pronunciation skill.