According to this answer, it seems as though staying up late is somehow a correction for Bnei Yisrael sleeping late. I've heard it explained that they thought nevua would only come while they are asleep, and thus sleeping through that morning would allow them to receive the Torah.
Given all that: How is staying up late (and, consequently, sleeping a lot the next day) somehow correcting that mistake? If anything, it would cause us to repeat that mistake as many people end up sleeping most of Shavuot day due to it.