[gambiting]

>>Flight recorders aren't designed to float and broadcast their position, or at least release a small beacon that would give rescue teams a general idea about where to search.

They are not designed to float, because there is no guarantee that the flight recorder will separate from the rest of the wreckage, but most importantly because accidents at cruise altitude are incredibly rare, it's the safest time of the flight - and you are very unlikely to be over the ocean in any other mode of flight. Even with airports close to the sea, a crash few km from the shore would not be difficult to locate.

And flight recorders have auxiliary batteries and actually broadcast their location for a month after the crash - the problem here was that no one had an idea where the plane crashed, something that's very,very improbable in its own right.