So animal first to have brain which does not need to rest would rule over everything else .
Again, you are assuming a few incorrect things:
1. That not sleeping is better for survival than sleeping to the point that any organism that had this trait would outperform any other organisms so much as to dominate every ecosystem.
2. That brains are the only organs that benefit from sleep.
3. That there aren't any organisms that do not fully go to sleep (dolphins are an example, they sleep with half of their brain at a time)
You also don't need to conserve energy because everything which has to sleep will sleep and you can kill and eat it with ease .
Why are you assuming that every organism that does sleep like we do sleeps too deeply to be awakened by the noise of something entering its shelter? Why are you only trying to apply this to predators?
Furthermore, have you even considered food availability? Lots of organisms simply do not have the luxury of a consistent food supply such that they can run around and be active all the time. This is why so many organisms go into hibernation for winter and other forms of stasis; if they don't, they will starve to death.
Being awake and running around more often as a result of never sleeping means more food is required per individual. As a result, ecosystems automatically could not support nearly as many members of such organisms as those which conserve energy through sleep. For example, a human sleeping usually won't burn more than 70 Calories per hour. A person sitting burns around 102 calories per hour. Being awake and burning that much and more energy per hour isn't going to make crops grow faster, now is it? It also won't make prey animals breed faster or more frequently. How much food is available to be had is finite and will not increase with more hours of wakefulness, especially considering the fact that plants need sunlight in order to produce food.
Then you can eat it and feed more energy to your brain that it would "gain" by turning your body offline for 8 hours to conserve energy .
Assuming the average person is a complete couch potato, the average person should go through 2192 Calories per day, including 8 hours of sleep. if they don't sleep, that makes it 2448 Calories per day. That's the difference it makes if all a person does is sit around when they are awake. That's for doing absolutely nothing productive.
Sleep cycles show a design , you can't evolve a sleep cycle because if sleep cycle worked then you keep it , if it did not work well you are dead and can't pass that information to your kids because you are being omnomnomed by belly juices .
-_- you know that if you consider sleep to be detrimental and then say it is a sign of design that this implies that you think evolution should result in organisms better at surviving than a designer making organisms would. Also, in a lot of organisms, sleep is just slowing down activity, they don't go through the same sleep stages we do. REM sleep especially has a strong correlation with intelligence in organisms. It's not like your body is doing nothing when you are asleep; many important processes, including memory processing and healing, are done while you are asleep. Your body needs your muscles, etc., not to be using up energy so that it can be directed towards these processes, which is why insomniacs often suffer from various health problems.