It seems totally logical that they should have a configuration option that if Logging is turned off, to have the GPS shut off with a custom delay (I would pick 1 hour) after you either shut off the camera switch, or after it auto powers down. When it powers back up, it starts with the same GPS it had at shutdown, so often it's not far off. I would gladly live with my first shot or two not perfect rather than a dead battery nearly EVERY time I pick up my camera.
IMO, Canon's GPS implementation is worse than half-assed. I'm not even sure if it is quarter-assed. Don't get me wrong, I like having it, but I'd like it a lot better if the people who implemented it had taken the time to do it right instead of saying, "Okay, we have data, ship it."
The 6D's battery has about 13,000 mWh of capacity. If it is running down in a week, the camera is drawing almost 80 mW continuously. Given typical GPS power draw, that suggests that the GPS hardware is acquiring fixes pretty much continuously, which is just completely and totally brain damaged, IMO.
In an ideal world, the camera should continue grabbing coordinates normally for a user-controlled period of time after you power it off (15 minutes, by default). After that period, it should grab coordinates only about once every 45 minutes so that the ephemeris data is always up-to-date, and so that its last known location is close enough to pretty much guarantee a hot start (unless you're in an airplane).
Powering up for a five second GPS fix once every 45 minutes should require very, very little battery power. Even with some of the worst GPS chipsets, that should take less than 1 mWh per hour. So by doing a single fix every 45 minutes, a theoretically perfect battery should last for somewhere on the order of 1.5 years in standby mode, not counting any other current draw for writing the data to flash.
Of course, the battery's self-discharge rate would likely run the battery down in less than a year, but that effectively means that the GPS's power consumption should be lost in the noise.
Also, in an ideal world, if GPS coordinates aren't available yet when a photo is taken, the camera should try to retroactively compute the coordinates after it obtains a lock, or at least write the coordinates into the EXIF data of recently taken photos after it obtains a lock, but that's another bug for another day.