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If we're positing users clever enough to modify the client, then such users could also just modify the client to scramble all CP images so that they would not be detectable via fingerprinting and can only be descrambled by a patched client.

People sending CP through whatsapp/FBM are not clever. If they were clever, they wouldn't be doing that. The justice department is not primarily interested in catching clever criminals, at least not via this particular mechanism.