If it's connected to the aircraft electrical system, it can still be turned off. There's a breaker somewhere, accessible to the pilots.
I read an analogy elsewhere that I thought was appropriate: Would you want an electrical circuit in your house that you couldn't turn off, especially if two rooms were full of jet fuel?
These satellite trackers are not high power. They use the same satellites that carry satellite-telephone traffic. So give the device a small battery which is kept charged by the aircraft electrical system, but which can maintain pinging for several hours without outside power. Then put it in the upper tip of the tail, where it can't be gotten to by hijackers during the flight, and where it won't bother anything else.
At the very least, a tracker which pings every minute or two will immediately indicate to the airline when the plane departs from its flight plan, and where it crashed to within a few miles. Add a software instruction to the GPS, which makes it ping outside of schedule when the unit's altitude changes by more than 5000 feet from the last ping.