Broadcast the second tx. And don't spend the original coins.
Broadcasting the second transaction won't work, since it is invalid.
It will be rejected by the network. So it would have to be stored on a server or something like that.
That's it. Now he only needs to create a "switch" to spend his coins to the address A whenever he dies.
The whole thread is about creating such a 'switch'. Your 'solution' unfortunately isn't a solution. It is just a different approach which still needs the key element, the 'switch'.
A button on his phone when he's on his deathbed, or something.
And what if the phone gets stolen ?
Of what if it breaks ?
Or what if he gets ran over by a bus ?
This definitely has to be done automatically. Therefore the timelocked transaction. If the owner isn't intervening, the transaction will be valid (the 'switch').