"So seriously, why do I have to sleep? Can you fix that yet?"
I love neuroscience speculation. The fewer citations, the better. Why? Because early on, before we really understand, everything is so simple. We have only a few points of ambiguous or anecdotal data, and from there it is easy to draw a nice picture that explains the world and puts everything in perspective. It is effortless and satisfying; the candy of science. Nevermind that the real situation is always more complex and less elegant. Nevermind that this is all superficial, unsupported conjecture. Nevermind there's a good chance it's entirely incorrect. Just enjoy the candy with me.
As you go through your day, your brain accumulates short-term memories in the form of new synapses. The presence of these memories (synapses) causes your brain to become more active and use more energy. As memories build up, they require more and more energy and it becomes more and more difficult to store new short-term memories (see "synaptic homeostasis hypothesis", particularly this article). At the end of the day, your brain is more active, fizzling with new memories. This state is both exhausting and non-ideal for learning.
When you sleep, your brain re-activates all these short-term memories over and over in order to commit them to long-term storage. At the same time, it removes many of the synapses that were created during the day. When you wake up, you have a blank slate; you are ready to form new memories. Your brain is calmer, quieter, and uses much less energy.
This may partially explain dreaming -- your brain recalls bits and pieces of short-term memories and plays them out to long-term memory. But because the pieces are recalled in isolated chunks, out of order, in the wrong combinations, etc., your brain has room to 'read between the lines' and construct novel stories around them. (This kind of creative dreaming might also act as a simulator where we get to try out (and learn from) dangerous things without consequences).
It explains why, when learning a new kind of task, you will tend to dream more about that task at night. After you have learned the task, your brain understands that it no longer needs to spend so much energy memorizing it. It explains why small children need to sleep so frequently--literally everything they see is new and it is completely overwhelming.
The problem may be that in order to move short-term memories to long-term, you have to think about them. And because the process of storing long term memories is so slow, you have to think about them for a long time. Most people can't be bothered to stop what they're doing every 5 minutes and memorize everything that just happened, so we store the memories up (at the expense of energy and brain function) and dump them all at the end of the day (when presumably, there's not much else to do since the sun is down).
Another problem may be that memories are difficult to isolate--the brain cannot automatically separate the short-term memories you are actively using from those you are ready to put away. Perhaps when you sleep, all short-term memories are stored and erased equally, so the time it makes the most sense to do this is when you are 'done for the day'. Of course, you can do it more frequently if you like; that's what naps are for. There are some species of songbirds that learn their song from their parents one play at a time--the parent sings the song, the child listens intently, then takes a 5-second nap.
So can it be fixed? Probably not without better hardware. There are a variety of drugs that claim to allow longer periods of wakefulness, but I would be cautious about these--there's a good chance they will have some effect on long term memory, so you get to stay awake at the cost of learning less (not to mention other harmful side effects).
On the other hand, perhaps most of the memories we store are totally useless anyway.
