At that point, you are trying to remove the ability to read the old files on the disk you are about to use for new encrypted data. Wiping with all zeros will make it extremely difficult to recover files and random will be even more so. But by writing down zeros, you leak metadata about the encrypted parts of your drive. Zeros almost certainly don't contain data, but the noise will. If I can see you have 30gb of noise on a drive, rest zeros then I know something I probably shouldn't, namely that you have written at least 30gb to that drive. But that same 30gb of noise wouldn't be discernible in a drive full of random data.
What you might be thinking of is when decommissioning the drive after having encrypted it. At this point, I don't think it matters. I'm not sure drives come with all zeroed status from the manufacturer anyways.
Buy a used platter of off eBay or from your favorite reseller of refurbished equipment (and keep the receipt). Replace the disk's controller with one of your own (the one it came with was broken). Ummm, I dunno what the previous owner of this drive has done with it!
Yes, that's what I meant. It's possible that merely having some forms of data in your possession would be considered prima facie evidence of crime -- there is no need for the state to demonstrate that you put it there or that you had any idea it was there to be convicted. That you might take content from somewhere and not look at what it is before carrying it is reckless -- and much like carrying, through airport security, luggage packed by someone unfamiliar to you.
What you might be thinking of is when decommissioning the drive after having encrypted it. At this point, I don't think it matters. I'm not sure drives come with all zeroed status from the manufacturer anyways.