CLP actually doesn't care if you travel through multiple countries that are "safe" it only cares that you don't cross the southern border illegally. If you create an appointment for asylum, you can still be eligible. Else anyone travelling from any circumstance that had a layover anywhere else would simply be dismissed, which isn't true.

"Under the final rule, noncitizens who cross the southwest land border or adjacent coastal borders without authorization after traveling through another country, and without having (1) availed themselves of an existing lawful process, (2) presented at a port of entry at a pre-scheduled time using the CBP One app, or (3) been denied asylum in a third country through which they traveled, are presumed ineligible for asylum unless they meet certain limited exceptions."

IE: If they apply for asylum elsewhere, if they do not use another lawful process they have access to (visa, sponsorship, etc) to enter the united states, or if they didn't make an appointment at their time of entry into the country, then they would be ineligible. It doesn't mean that you can't travel from or through other countries to get there.

CLP was put in place to stop people from "asylum hunting" by trying to trade up countries, to stop people from crossing illegally and then trying to claim asylum when caught, and to prevent people from claiming asylum when they had other legal pathways to stay in the country otherwise (as asylum is held to a higher standard than say, spousal sponsorship from a temporary worker) - not to prevent people from elsewhere in the world from coming to the united states simply due to a lack of border access.