com.google.android.gms destroying my battery
Thanks to the logs, I found the culprit: the bad (maybe even illegal?)  practices of Google Maps. 

Since I hate spam and hate to be tracked for advertising by Google, I always opt out for all those things. In the last version of Google Maps for Android, there is a Location History option, that was off. Since Google Maps has the devilish behavior of trying to track you by launching itself when you don't open it yourself, it opens in the background and tries to save your location in their servers. That trigged a crazy loop because of my Location History off setting. 

The only solution I found, at least if I want to keep using Google Maps, was to enable Location History. No more batery drains. 

Google is copying the worst practices of Microsoft at the speed of light.