What my Paint breeder friends told me is that there are a number of older (well, I'm older, too) APHA judges that had been AQHA judges and they prefer the the standard QH coloring horses, and therefore prefer the minimal white Paints.
Our tovero mare, Lady,
is such a Paint with a lot of white that a 'brown biased' judge may not like. Her sister (that looks like her twin) has done well in Paint halter classes, though.
As for keeping them clean, having 3 Paints, it really seems to depends more on the underlying skin and type of hair than the color. Lady, above, has very light pink skin and fine hair...If she stays in the summer sun all day, she can burn without sunscreen and she is VERY difficult to keep clean unless it stays dry for a week (grass stains are the worst).
Angel, our tobiano, has thicker hair and her white is easy to keep clean (for some reason). Even if she gets muddy, a quick curry and brush gets her white again.
Our young overo, Cinnamon, doesn't have much white, and although in this picture she has her very shaggy winter coat, is very short haired and very easy to keep clean (even her stockings).
BTW, I know that baby powder is a popular last minute 'touch up' for white on Paints.