The brain is a muscle. So it can be trained and will also require rest afterwards. I have noticed that I get a deeper sleep after a good exercise, so I can understand what you're saying. It's interesting that your brain is looking for more work instead of sleeping, which makes me think you trained it too hard before and is longing for the extra thinking.
I think it is the opposite! I wasted it during the day and it is looking for a way to be better utilized, even though bed time is the wrong time for it.
Just imagine if we used our thoughts at full effectivity. I wonder what is possible.
I think balance is important. I have heard the myth that humans only use 10 percent of the brain loads of times. The truth is we use most of it efficiently. I think if we fully concentrate all the time, we might overheat.