You still get an enormous amount of sugar, with or without the pulp.

Regarding the vitamins and minerals, my understanding is that you need a certain amount of each of those to avoid various nasty and fatal diseases, and an amount over a certain limit can be poisonous, but there isn't any real evidence that anything in-between makes a difference. From what I understand, it also requires a very extreme diet (by modern developed world standards) to develop provably harmful micronutrient deficiencies.

(One exception might be vitamin D if the winters are especially dark and cold where you live, but you won't get that one from fruit juice.)