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An encrypyted drive is likely to have (close to) equal numbers of 0's and 1's full or empty so any of these arguments are moot.


If the drive isn't encrypted, is it possible that controllers use some kind of encoding to balance out the number of bits, so that there's not a long run of 0s or 1s?


Yes, this is necessary for high density NAND flash and is referred to as "whitening" or "scrambling". Not needed at all for SLC or older MLC.




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