The point of using random instead of zero is that it's harder to see which parts have been overwritten and which parts haven't been.
Since the worry seems to be speed, here's a tool I wrote to get random bytes about as fast as drives can accept (well, at least spinning disk drives, there might be some flash drives that are faster):
https://github.com/pflanze/fastrandom
I'm expecting you to figure out where this tool goes wrong and produces predictable bytes yourself. Also, please tell me if you do :)
Anyway, even if it isn't secure, it will be enough to foil compression algorithms.
"Give us the encryption keys" "It's not encrypted, I used /dev/urandom" vs "Yes, I wiped it"
And random data is very easy to see.
The people who propose using multiple overwrites are clear that they're talking about making it harder to recover bits. (They're wrong, but it's what they say.)