I think it'd take more than picture quality to make classic films accessible. Acting styles and pacing especially have changed a ton since the b&w era. It's not to say they're not good, but they're a bit of an acquired taste.
A kid in this house has started an appreciation for the original Twilight Zone, and enjoyed Casablanca before that. Gotta start early I guess. TV is scarce in this house, which promotes reading and feeling lucky to see a great movie, no matter the era.
"Sometimes" is the right word. Usually, it's just inferior. B+W was used for artistic purposes only rarely, the rest of the time it was because it was cheap and easy.