Am I missing something or is the "carry around signed TX on paper" part just a way to make this more complicated without gaining anything?
Not quite. With his plan, someone has to steal both his (physical) wallet and his phone (and then spend/transfer it before the rightful owner realizes the theft and transfers the coins elsewhere) in order to steal his coins. This is of limited use since the wallet and phone are typically carried on your person, but at least it protects against digital-only attacks, and some in-person theft scenarios.
While it might* reduces the risk to some form of attacks, I would argue that they are so uncommon that the missing comfort is worse. Esp. since youd only carry around what you would otherwise carry around in a regular wallet anyway. Id also think that a regular thief would turn the phone off ASAP to avoid any sort remotly controled tracking software. Its not like a thief would specifically target someone using bitcoin.
I'd add that you should encrypt the transaction with a passphrase/password before writing it to the paper. Unfortunately, this further complicates the retrieval process: you need a decryption app on the phone. But it does mean that the paper is useless without something that only exists in your head. In this case, you could even store the TXs digitally on your phone and/or the Internet, since there is no longer a security concern.
The app should offer some form of encryption anyway. A simple 6 digit PIN like mycelium uses would be enough to go home and recover the coins.
PS: * I just realized that with a presigned TX the coins have to go to a known address anyway (e.g. your own phone) thus you do not even gain anything in case of an infected phone. There might be certain circumstances where you discover that your phone can no longer be trusted but do not have broadcasted the paper TX yet. I think we are officially in tin foil hat land now.
Just send the coins you want to spend that day/night to your phone and send back what you have left when you are back home.