Parfit's Hitchhiker; in the future, after having observed that you've already been picked up and made it to safety, you'll still compute the counterfactual "If the output of my computation were to refuse to pay, then I would not have been picked up."

Since TDT screens off all info that goes into your decision-setup, using your updateless version of TDT might obliterate the difference between evidential and causal approaches entirely - no counterfactuals, no updates, just ruling out of self-copies that have received incompatible sense data. (Not sure yet if this works.)