I am ready to change my opinion about this style of reasoning, but probably I need some more powerful intuition pump.

I don't know if this is exactly the kind of thing you're looking for, but you might like this paper arguing for why many-worlds doesn't imply quantum immortality and like-minded conclusions based on jumping between branches. (I saw someone cite this a few days ago somewhere on Less Wrong, and I'd give them props here, but can't remember who they were!)