Nope, you're thinking of this backwards. The people who actually have something illegal to hide might actually try to do what you're saying here, make it untraceable somehow (at non-trivial risk and expense, of course!). But if what you're worried about is more casual, warrant-less invasion of privacy by your government (that isn't motivated by something as blatantly illegal as the examples you chose), "just store it at home" is a no-brainer.