The problem with checked luggage first arises if somebody doesn't get onto the plane in time even though their luggage has already been loaded. This essentially means that somebody has to look through all the (already loaded) luggage to remove that specific piece, which, depending on how deeply it's buried, might take considerable amounts of time. This isn't a problem with hold luggage, since there cannot be any hold luggage aboard a plane without a corresponding person.
This isn't a huge problem for Southwest though, as checked baggage for domestic flights do not have to be pulled (and rarely ever are) in the United States. It'll be stored at the final destination printed on the tag until you pick it up, or you file a baggage claim to have it sent back.
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This isn't real analysis. However:
The problem with checked luggage first arises if somebody doesn't get onto the plane in time even though their luggage has already been loaded. This essentially means that somebody has to look through all the (already loaded) luggage to remove that specific piece, which, depending on how deeply it's buried, might take considerable amounts of time. This isn't a problem with hold luggage, since there cannot be any hold luggage aboard a plane without a corresponding person.
This isn't a huge problem for Southwest though, as checked baggage for domestic flights do not have to be pulled (and rarely ever are) in the United States. It'll be stored at the final destination printed on the tag until you pick it up, or you file a baggage claim to have it sent back.
As the other poster alluded to, this is no longer a rule for domestic flights inside the US now that 100% of bags are screened.
It still applies to international flights (presumably for customs reasons).