Why are there not two sets of CVR and FDR, one at each end of the aeroplane ? There are backups for lots of other systems.
The recording system on a typical aircraft consists of 1001 sensors all over the aircraft,
a box for collating the data (typically just aft of the cockpit where most of the airplane computers and sensor analysers are*), the recorders in the tail, and a number of power supplies to drive these devices. A system is really only as strong as it's weakest link. Such a catastropic event where the aircraft is breaking up in flight will (IMHO) not give much additional data. Whilst the data module of recorders are able to survive fire and 3400g crashes, obviously the other components of the system are not designed to survive a fraction of this.
The recorders are usually powered by normal aircraft power (not batteries). Even if you made the CVR/FDR battery powered, you still need power to the other 1001 components to get all data.
*Probably to minimise length of databus wiring.