Many cars already have EDRs, such as the much maligned Toyota unit, which is a closed system, and can only be read with Toyota tools.
The way the EDRs work is that they write data to flash memory in the few milliseconds before, during, and after a safety event, such as an airbag deployment. They typically have a large capacitor onboard, which provides a little bit of power so the unit can finish writing the data if it loses power during a crash.
I think it is unlikely that NHTSA will mandate that car EDRs be made to the same deep submersion and high temperature survival specs that airplane black boxes are made, as these are much less likely to occur in even a very severe car accident.
What may be required is a larger capacitor or a backup battery to keep the thing running longer after losing powere, and more memory to store a longer trace. For example, if the unit needs to store 64 bytes of data at a very vast 1ms rate, a minutes worth of data would require about 3.8 MB of storage. So we are talking about a few dollars worth of flash memory, and maybe another few dollars for longer term keep alive capability.
I could see the cost of EDRs going up by, say, $50-$100 per vehicle. But not $5000.