Sorry, I thought you were someone else, so my first reply didn't make sense. If the private key is never exposed to the network, why in your original comment did you say that
you should withdraw all funds only once, spending everything. This
is because in the process of unlocking and spending funds, you ex‐
pose the private key
?
We have been describing creating and spending a paper wallet as if it were a top secret Area 51 procedure. It is wise to be secure around money. One needs to use the Private Key for a cryptographic signature in order to sweep the paper wallet of bitcoin. Someone could be looking over your shoulder. If you imported the Private Key to an online wallet, a hacker might grab it. If you sweep the account on a bitcoin wallet client, there is the danger that a hacker is recording your keystrokes, moves faster and sweeps your account before you do.
The mere fact the Private Key exists means it can ultimately be compromised.