Yeah, blackwalls suit many bicycles, especially earlier examples and non "glammed/blinged" to start with. Not all vintage bikes (40's thru 60's) came with w/w tires. Generally the fancier top end bicycles came from Factory with whitewalls, ( much like cars of that era) the Schwinn Black Phantom being one of them.
Not to say what is right or wrong. It's a personal taste in part. I ( am into vintage cars/motorcycles too) am partial ( prefer) whitewalls on my bikes/cars, but that's generally what they came with.
To see a 1960's muscle car with wide whitewalls or a 1950's vintage ride with thin redlines is just WRONG. ( but not a big deal) The same goes for bicycles. There is a wealth of original and reprinted literature that can be used for reference. In the end, it's what makes you happy/you get the look you want. If a person wants "original" and to show it as, it's worth doing your home work and representing as such.
Lots of my bicycles are slightly "custom" but that's what people did back in the day too. My cars and vintage motorcycle are as close to stock as I could go. That's a personal choice.
Cheers,
Bob