Let's counter his arguments: how often has a paper wallet leaked millions of customer addresses?
Not really a fair comparison. How could a paper do that?
Consider this scenario:
You said you have a printer without WIFI. Maybe you bought it with cash, maybe with a credit card that shows your real name. That information is stored somewhere on a server. The shop gets hacked and the data gets leaked. Does that make your product (the printer) worse? Would you stop using it and throw it away?
Although Andreas is advocating for the use of hardware wallets (I think he even mentioned ColdCard in the video), the point is to stop using individual private keys and back them up. Too many mistakes have happened that have caused people to lose money by not making a proper backup of their private key, using bad software solutions that send change to a different address whose private key you don't have, etc. Instead of that use HD wallets and forget about single keys. Hardware wallets happen to be a good compromise between security and simplicity.