We don't have 4G, but I am worried that it might be pinging something constantly looking for it. Should I be worried about that? I have LTE OnOff, but I have had a couple of problems getting texts and calls when it is not in the default mode.
Unless you are right on the edge of an LTE area I wouldn't worry about it. I'm in a 3G-only town and have never bothered switching it off - my battery regularly lasts me through the day, and did even before I rooted and started messing with stuff.