My assumption is that a cheap black and white laser printer doesn't store anything after I cut it's power. But if you're really worried about that, make sure the printer never leaves your house. Or encrypt the wallet before printing.
I don't know if anyone saw what SeedSigner is doing for manually backing up wallets with QR codes that are drawn with a pen, instead of using any printer.
This can be done at your own home and no machine will be used, you just follow instructions and fill up empty squares with permanent marker or pen.
This QR code for example contains twelve word seed phrase, and entering this code will import your seed words:
https://www.youtube.com/watch?v=c1-PqTNx1vcand for the rest of your life, not keep the paperwallet at home.. because you dont trust family to not find it a day, week, month later laying around the house.
It's more likely that even if your family finds your paper wallet they won't know how to use it, or if you used bad printer they wont find anything because ink palled like we see in those thermal receipt printers all the time.
Regardless of the audience, claiming that paper wallets are obsolete is pretty misleading. In fact it is more misleading if the audience is at beginners level or doesn't understand much. They should be educated on why and when a paper wallet is insecure or doesn't provide the functionality that you would want (single private key compared to HD wallets). And more importantly they should be told about what they can do to improve that.
He was talking for years and educating people why paper wallets shouldn't be used my masses anymore, and this is not his first video about that subject.
It's easy to find all his previous videos and I am sure you will find that he explained several times what you are talking about.