I agree that the FDR/CVR should not consume power to the detriment of occupent safety; obviously. I still would have thought in this day and age it should be possible to maintain both.
Although not directly applicable, look at the controversy surrounding the Mull of Kintyre Chinnok as a result of having no FDR/CVR at all. Not fitted or not powered; the outcome is the same (lots of extra work, speculation and possible controversy).