Yeah, I follow. I'll bring up another wrinkle (which you may already be familiar with): Suppose the objective you're maximizing never equals or exceeds 20. You can reach to 19.994, 19.9999993, 19.9999999999999995, but never actually reach 20. Then even though your objective function is bounded, you will still try to optimize forever, and may resort to increasingly desperate measures to eek out another .000000000000000000000000001.
Yes, this would happen if you take an unbounded function and simply map it to a bounded function without actually changing it. That is why I am suggesting admitting that you really don't have an infinite capacity for caring, and describing what you care about as though you did care infinitely is mistaken, whether you describe this with an unbounded or with a bounded function. This requires admitting that scope insensitivity, after a certain point, is not a bias, but just an objective fact that at a certain point you really don't care anymore.
Edge.org has recently been discussing "the myth of AI". Unfortunately, although Superintelligence is cited in the opening, most of the participants don't seem to have looked into Bostrom's arguments. (Luke has written a brief response to some of the misunderstandings Pinker and others exhibit.) The most interesting comment is Stuart Russell's, at the very bottom:
I'd quibble with a point or two, but this strikes me as an extraordinarily good introduction to the issue. I hope it gets reposted somewhere it can stand on its own.
Russell has previously written on this topic in Artificial Intelligence: A Modern Approach and the essays "The long-term future of AI," "Transcending complacency on superintelligent machines," and "An AI researcher enjoys watching his own execution." He's also been interviewed by GiveWell.