You don't change the utility function because it makes decision making more convenient [..] someone who does care just as much about each additional person would be making an error if they acted as if they had a bounded utility function.

True.

That said, given some statement P about my preferences, such as "I assign linear value to person-lives," such that P being true makes decision-making inconvenient, if I currently have C confidence in P then depending on C it may be more worthwhile to devote my time to gathering additional evidence for and against P than to developing a decision procedure that works in the inconvenient case.

On the other hand, if I keep gathering evidence about P until I conclude that P is false and then stop, that also has an obvious associated failure mode.