The reason to pay anonymously is so you keep the anonymity throughout the whole process. If I pay for a VPN using a standard method, there is now a transaction saying I gave money to XYZ company that happens to be a VPN provider. Said VPN provider eventually gets seized by the government, and even though they said they did not log anything, perhaps someone did a configuration error, or it was in debug mode, and it was indeed logging, now they can tie that credit card transaction with my VPN account, and perhaps get the VPN keys and such that way.
I may just lean towards the gift cards though. Can buy those with cash, then they are pretty anonymous. You will show up on CCTV, but so will everybody else that bought gift cards - do it around Christmas. If you don't use it right away it's pretty much near impossible to track. Most stores don't keep CCTV footage forever either. The odds of actually being tracked that way is slim to none, but still stuff to consider.