First it's important to know that relative to desktop operating systems like windows, it's extremely easy for one to call themselves a developer for a mobile OS.
Therefore when Android first arrived, these novices began poking around in Android and noticed that just like a PC, some tasks were running in the background.
What they wrongfully _assumed_ is if they "killed" these, the battery life would be increased. They also assumed that the processor would be free and speed up the phone. Both assumptions are wrong.
Why did they make this mistake? They failed to study how Android works and rushed into hacking it. Most of the apps in the background are simply idling waiting to assist in launching an app you're using off and on. They actually speed up what you're doing They are supposed to be there & they are not drawing power.
Why are so many adamant it increases battery life and makes the phone faster? Placebo effect. Plain & simple. There are no quantifiable tests to prove their claims. Any set of benchmark results can be manipulated and that's what's been done to save face.
Cheers