I think I may've found a resolution to this problem. At least it worked for me, on both phones that I have. I started with "Android System" using 40% and "Android OS" over 30% on each of my phones, and now they're all at 4%.
The problem definitely seems Wi-Fi related, but turning Wi-Fi alone is just a temporary fix. Here's what I did:
1. Turn the Wi-Fi off, then wait few minutes and turn it back on.
2. Let you battery drain completely - play some games if you want to speed it up, or just wait, but DON'T CHARGE when prompted. You have to let your battery drain completely - let the phone die on you from the lack of power.
3. Charge the phone fully. Don't disconnect the charger until you see the icon in your status bar that shows the battery has been charged completely. You can use the phone while charging, if you have to, but it'll charge faster if you don't.
4. If you now check the battery use, you may still see the same results as before, but just use your phone a bit and come back and check later, and you should be good.
If this doesn't work for you, do this again but this time after resetting Wi-Fi (step 1) turn the phone off and remove the battery for a minute. Then continue to step 2-4.
Let me know if this helped you. I'm curious.