Under kit-kat I usually got 3-4 days on a charge, and never paid it much attention, but under lollipop it dropped to 1-2 days. The culprit was Google Play, which was running 43% of battery drain, and Google + another 23%, plus another big chunk for the google updater, and my battery was running down quickly. Now, it happens that I use my phone for only a few things, phone calls, texting, email, calendar, and once in awhile I browse the web or take a photo, plus a few apps like flashlight and calculator. I don't do any social media things, so I really have no need for the Google Services, so I undertook to do exactly what you suggest, stopping the google stuff from whatever it was doing, and the difference, when I finally succeeded was huge.
So.... how could I stop the google stuff? Well, I went to Settings-Mobile Data and set it so that app updates, google play, etc, can only update via wifi... then I turned WiFi off. I will turn WiFi on while charging, and they can catch up at whatever they do, though I have no idea what that might be. Next I went to settings-aps, and uninstalled Google +, while reset it to factory state, then I made sure it was disabled. I also made sure that Email, Gmail, and my Calendar weren't trying to refresh unless I told them to, which is the way I normally use them anyway. Also, I have GPS off, as I always do, since I don't use it.
After these changes, my usage shows :24% screen, 21% phone idle, 18% cell standby, 12% android os, 5% Android System, 5% voice calls, 3% Smart Device Manager, 3% Google services, 2% Swype, 1% Phone, 1% Chrome. I currently have 103 hours on this charge, and am down to 12%. It estimates that I have 14 hours left. Because I don't use my phone in the evenings or overnight, it will last longer than that, probably 18 hours, for a total of 121 hours, just over 5 complete days. Note that this is a two year old G2, so it isn't like the battery is new.
Have I had any problems? Honestly, I haven't noticed any difference at all, other than extending my battery life from 1-2 days to 5 days. I have no idea what Google Play and Google + were doing with all the power they were using, but it doesn't seem to have been anything that was of any use to me.
Oh, and the other change I made was to get rid of those horrendous messages on the lock screen, describing all this "sensitive" stuff that was going on my phone, which made it look like I was up to something. Thankfully my LED notification still works, and that's really all I need.