Rabbi Yaakov Chaim Goldwicht z"l (אספת מערכות פרשת יתרו - sorry, no available link) has a lengthy and deep lecture to explain why they felt it important to sleep. Without delving into his words again, this is in short, and on a superficial level, the way I remember them. Any unclarity is my fault. The reason why they went to sleep was not due to an indifference to the forthcoming Revelation. On the contrary. They thought it was an essential preparation. Whilst awake, we can only achieve a limited amount of Torah knowledge, as our physicality acts as a wall between the spiritual world where the knowledge of תורה resides. That barrier disappears greatly whilst asleep, which is why all prophets, besides Mozes who was constantly on a high spiritual level, received their prophecies in a stage of sleep/trance. The knowledge attained whilst asleep can then be further developed upon awaking. In fact, many Torah giants throughout all generations, after they had toiled in Torah with all their might during the day, but were still left with unresolved questions, merited to a solution to their questions during the short sleep which they allowed themselves. To be sure, this only applies to people who use their awake hours to toil in Torah. Those who waste their days, will not become more knowledgeable whilst asleep. The Jewish people had travelled 49 days towards the giving of the Torah. During all that time they were preparing for that great Divine Revelation. However, they thought that they would be incapable to be grasp those high revelations whilst awake. Whilst their body was “dressed” on their soul. And indeed, when they eventually heard the first words of the ten commandments, they, in their physical state, couldn't cope with it. That is why they went to sleep. But they were wrong. The words of Torah can only be handed over with the full cooperation of the recipient and for that one has to be awake. What made them make that mistake? Here human nature comes to play. Perhaps, deep down, there was an element of laziness involved. By staying up Shavuos night we want to be repair that small element of laziness and thus merit to absorb the full measure of spirituality our soul is capable off.
