I, along with all of you can't understand the split.
The show type dog can't do the field work. But they consistently win for how they look. The people producing the show type dogs are working hard and have spent many years trying to get that look. I'm sure they are very dedicated to their "game" and know what they want. The show judges are rewarding their efforts. The standard has been changed fairly recently according to what I read here.
Labrador retrievers have been around for a long time. Long before they came here and ended up in field trials. There's a connection to Newfoundland dogs. Depending what version of history you read Labs came from them or they came from Labs. The show people always talk about coat and otter tails for water work. There's usually a reference somewhere to Labs helping fishermen.
Maybe the show people are trying to produce a dog that was around in the 1800's or earlier. Pre field trial if you will, or whenever pre field trial was.
I read something yesterday on the internet after a link from RTF along these lines but can't find it again.
It is about the only plausible explanation I can see to explain the difference between the field and show Labradors. Old type and new type Labrador retrievers.