If humans are the only advanced civilization in the universe, then there is no real need for a Universal Morality that applies to the whole universe. All we would really need would be a morality that applies just to the earth. But suppose we are not alone, and there are other advance civilizations in the universe. Then these civilizations would need a common morality as a basis to interact with each other.
Advance civilizations in the universe will eventually develop technology capable of creating weapons that can easily destroy any other advanced civilization. If they don't all follow Universal Morality (or an equivalent system), they will all eventually destroy each other. We know two methods of killing most of the people on our planet: nuclear weapons and biological weapons. We have only had these weapons for a relatively short time. Imagine what kinds of weapons we will have hundreds of years from now! Imagine what kinds of weapons other civilizations with the kind of knowledge we will have in hundreds of years might have! If all extremely advance civilizations in the universe know how to make weapons that can easily destroy each other, the only reason not to do it is a morality that says that all other species are equally worthwhile as your species.
This is how I discovered Universal Morality. I asked myself the question "What moral system would we want an advanced civilization from outside Earth who we met to follow?" If they believed that they were superior beings who were entitled to do anything they wanted to us, we would be in a lot of trouble. They could treat us the way we treat our most advanced species, such as monkeys, as beings with virtually no rights, whose primary purposes are either for our experiments to help us develop ways to make our lives better, or for our entertainment. It might serve us right if advanced beings came to earth to collect us for experiments, food, or entertainment, but I hope these beings are more morally advanced than that. I hope they follow Universal Morality, and treat us the way we should treat all animals on earth, not the way we actually do treat those animals.
Any advanced civilization in the universe is in a race of technological advancement against moral advancement. If the technology advances to the point of quick and easy access to weapons that can destroy the civilization before the civilization develops a morality that keeps these weapons from being used, then the civilization will destroy itself. Therefore, I think that Universal Morality may be a natural cultural development of advanced civilizations in the universe. The civilizations that don't adopt UM destroy themselves, and the civilizations that do adpot it go on to develop extremely advanced civilizations that we can barely imagine. These civilizations would care about each other, and about all other sentient creatures in the universe.
Although mutual fear among nations has worked so far on earth to keep nuclear and biological weapons in check, this is not a workable long-term solution. Right now, these weapons are in relatively short supply and are relatively hard to make. When technology becomes so advanced that any determined group will be able to have these weapons, it will only be a matter of time before a group that isn't afraid of retaliation has some of these weapons, and the desire to use them. The same situation applies to advanced civilizations in the universe. Mutual fear may work for a time, but eventually has to fail, as soon as there is a group that isn't afraid.