Singers may try to sound like they think they're expected to. I don't think most people do that, but I don't know most people.

Regional accents are incredibly varied. Texas accents vary from super-twang all the way to "I'm from the northeast, and I don't hear any accent". I'm from NY state, and I can think of 4 distinct accents, and I know there are more. Some try to lose it, and some try to intensify it, probably for the same reasons they do in the UK.