I've run phones for weeks without restarting - with no problem. A stable Android installation doesn't require constant restarts. This is Android, not Windows. The entire design philosophy is different, the operating system works differently - the only thing they have in common is that they run on computers.
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Multitasking the Android Way. Unused RAM is wasted RAM. (One of the engineers who wrote Android should know how it works.) Killing apps only slows the phone and wastes battery - if Android wanted those apps not in RAM, they wouldn't be, some other app would be in that spot. (There's a huge difference between an app
being in RAM and
running in RAM. An app can be in RAM and not be running.) If Android needs a process in one of the apps it's going to reload it. The app killer will kill it. Android will reload it, etc., etc., defeating the design philosophy of Android, bringing the phone to a crawl and wasting battery.
Restarting an Android phone regularly (or once in a while "just because") just wastes the phone's battery and your time. And, yes, killing a needed app can cause an increase in battery use as you kill it, Android loads it, you kill it, Android loads it ... If it happens regularly, without killing any apps, it could be a defective battery.
Bring in RAM doesn't cost battery. (There's always SOME value to a bit in RAM - whether that's random or part of an app doesn't make any difference in battery drain.) Being loaded back into RAM because it was removed by something other than Android does. (If Android removed it [actually just used the space it had been in], it's because it wouldn't be using it again for a while.)
Don't ever kill an app's cache while it's running, unless you don't care about the data in the app. It might be holding that data in cache at the moment and if you clear the app's cache, you lose the data (like the essay you just spent 3 hours writing). System cache is another matter - the system will rebuild its cache as needed.
But you don't restart the phone to clear cache, you just go to Storage/Cache and clear it.