It seems to me we are talking about different things. The link given by the OP refers to stay-at-home situations, not wilderness travel in pristine watersheds.

I agree that boiling is preferable when an energy source is readily available.

I recall that iodine tablets were particularly unpleasant, but I used them for lowland situations where boiling was impractical and cattle had access to the rivers. As soon as reliable filters became available, I was happy to dispense with iodine altogether, and have no desire to look back.

I agree with the OP that is surprising that the link provided dismisses everything except household bleach. Other forms of chlorine (tablets, chlorine dioxide) seem to be acceptable for international travellers, as per this link:
https://wwwnc.cdc.gov/travel/yellowbook/2020/preparing-international-travelers/water-disinfection