I prefer writing the private key down on a piece of paper, instead of printing. Printing requires you to either transfer the data by WiFi or USB, for both you're not sure whether it will save anything on the memory, as it could then later by stolen trough the same communication protocol. I'm extra cautious because I use a shared printer, so a lot of devices get connected to the printer which could possibly be compromised. Handwritten paper backups are also the way I save my passwords, where I use a different one for every occasion. I use manually random generated passwords for accounts that have a lot of value for me, the dice works very good for this purpose.
Sure your points are valid about avoiding printing on public printers but the problem with writing such data by hands is that it is prone to errors. Humans make errors. Even copy-paste is not error free, you may paste some different data than you intended or skip a digit, but hand writing?
You know I had a cold storage once that I created by copy-pasting some data around, and when I was to recreate the wallet to "hot" it was an experience full of stress, I was not sure if it will work out as I intended. If I had had it manually written down, I would have been freaking out (!)
So if it is a nice sum of money, I wouldn't hide it behind a handwritten private key. Private key is long and we are only humans!
I really stand by my previous advice of using a hardware wallet to protect your money. And if it is a large sum, than: all the more
