Holding onto a pronounced regional accent "speaks" to a gratuitous egotism and stubbornness; winners do what it takes to get the job done. It's no moral compromise to have a neutral accent. it may even be a signal that you are not going to favor one group over another.
When I moved away to college, I eased out of my regional accent as soon as possible and adopted what I called "television announcer English." It made going through school easier, and it made doing business easier once I got out of school. Not everyone has an "ear" however for how they may sound to others; that's where a good vocal coach comes in. She needs one.
Gratuitous egoism is what makes people go into politics in the first place, even the good ones. I remember reading that Jimmy Carter had a speech coach in preparation for his intro onto the national stage. He would sound like an idiot speaking flawless French, but it apparently did help him to some degree. Some people can get away with it more than others. A strong vocabulary and good reasoning will make a big difference. I think it would help her to improve in this area.
Football coach and soldier are the two professions where a pronounced accent of almost any kind actually seems to be an indication of greater gravitas.