So in this case my question is why Kaj suggests his proposal instead of using bounded utility.

Two reasons.

First, like was mentioned elsewhere in the thread, bounded utility seems to produce unwanted effects, like we want utility to be linear in human lives and bounded utility seems to fail that.

Second, the way I arrived at this proposal was that RyanCarey asked me what's my approach for dealing with Pascal's Mugging. I replied that I just ignore probabilities that are small enough, which seems to be thing that most people do in practice. He objected that that seemed rather ad-hoc and wanted to have a more principled approach, so I started thinking about why exactly it would make sense to ignore sufficiently small probabilities, and came up with this as a somewhat principled answer.

Admittedly, as a principled answer to which probabilities are actually small enough to ignore, this isn't all that satisfying of an answer, since it still depends on a rather arbitrary parameter. But it still seemed to point to some hidden assumptions behind utility maximization as well as raising some very interesting questions about what it is that we actually care about.