Part of the reason is that neurons do not store glucose like many other cells in the body do. Also keep in mind that liver regulates blood glucose, so the brain can technically use energy that originally was stored in amino acids, fatty acids, or ketones through the process of hepatic gluconeogenesis, which would increase plasma glucose and therefore increase the amount of glucose available to the brain. If your liver is healthy and you have enough fat or protein available in your body, your blood glucose will never fall to dangerous levels. In fact, many amino acids are glucogenic, meaning that they can be converted to glucose in the liver. In a starvation state, many of the other tissues would redirect to use non-glucose fuel sources like blood ketones, leaving the majority of plasma glucose to the brain.
You also ask a good question about why this is useful in the first place. That's largely because of the blood-brain-barrier (BBB), which very tightly controls what can pass from plasma into the brain. Many important molecules, like glutamate, aspartate, and glycine, are potentially neuroactive, and therefore (in general) the BBB does not allow molecules to cross without going through molecule-specific uptake pumps. For example, glucose has it's own uptake pumps in the brain, entering the brain via GLUT1 or GLUT3 uptake pumps depending on the specific cell type. This extreme specificity not what happens in most other parts of the body, where endothelial cells are not joined by tight junctions like they are in the BBB. As a consequence, many important molecules that must be synthesized within the brain even when they're abundant in the plasma. Glucose that enters the brain can be used to synthesize many of those other molecules that can't cross the BBB - for example, glycogen from astrocytes is one of the sources of carbon for the synthesis of glutamate within the brain.
The specificity of the BBB really a great thing - the brain is very sensitive to many of the molecules normally found in your plasma, so the fact that the BBB is very specific and doesn't allow a lot of this other "stuff" in is protective.
If you're interested in learning more, check out a great article published in Trends in Neuroscience in 2013 by Philipp Mergenthaler et. al. titled "Sugar in the Brain: the role of glucose in physiological and pathological brain function."
Hope this helps! Feel free to follow-up with any lingering questions