This is a great question. A good place to start is with the political theory of the ancient Greek historian, Polybius. He states that there are three forms of government in our world: monarchy, oligarchy, and democracy. He also states that each form of government has positive and negative points. So, we need to keep in mind that monarchies have both positive and negative aspects.
Since this is a question on the benefits on monarchy, I will give you three. First, monarchies in times of deadlock can get the job done. Sometimes you need a strong leader who will break stalemates and push the nation forward. Second, monarchies are more efficient, because there are no opposing parties. So, there is the matter of efficiency. Third, in extreme times and extreme difficulties, you need a good monarch figure to straighten things out. The only times monarchies are less desirable is during good times.
Perhaps the most important benefit of absolute monarchy is that it can bring more stability to a country than a more feudal system often does. In a system where the monarch's power is less absolute, we often see terrible civil wars that arise as various of the more powerful lords jockey for power and try to position themselves, if possible, to take the throne. This is much less likely to occur in a country where the monarchy is more absolute and the power of the lords less relevant.
In addition, the absolute power of a monarch can be advantageous if the monarch is a good one. In such a case (rare though it may be) the monarch has a free hand to act as they wish without having to contend with obstacles set up by lords or a Parliament.
All this said, absolute monarchy does not seem on balance to be a very beneficial system.
It also gives more protection.