Black boxes are not designed for that purpose though. The primary point of a black box signal is to help you find the black box in the water, as you said.
If you get close enough you can track the black box to find the craft, but the range is so short, especially in the ocean, you really need to know the exact area where the craft is for it to help.
I was mistaken in one thing .. the depth it supports is 20,000 feet. The range is actually 1.2 miles.
A black box must be able to withstand many accident scenarios without sustaining damage. Before being put into use, they are tested to see if they can withstand an impact with a concrete wall at 750 kilometers per hour (about 466 miles/hour), a static load of 2.25 tons for at least five minutes, a maximum temperature 1,100 degrees Celsius (2,012 Fahrenheit) for one hour and water pressure found in depths of up to 6,000 meters (about 19,700 feet).
In order to be easier to find at sea, the devices send out a signal on contact with salt water that can be picked up within a radius of about two kilometers (1.2 miles). At such a short range, the location of the wreck should already be more or less pinpointed in order to find the device.
They really should have had a transmitter on the craft itself and one with a more powerful power source and a surface chase boat should be shadowing their location.