• limit U(1)→∞, P(chr)→0 P(chr)U(1) is undefined, and
• invoking infinite utilities isn't fair.

You can get these problems if you have only finite utility, but infinite expected utility.

It's impossible for a prior with a converging expected utility to result in a posterior with diverging expected utility using only a finite amount of evidence.

While it's correct that just using absurdly low probability and absurdly high utility won't cause that problem, it's not likely to come up without that problem being there in the first place.