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.
Often they're right. They'd be much more watchable with an AI that could sharpen the picture and colorize it.