::::::::Strange. Like other guidelines, WP:COMMONNAME pointedly says at the outset to use common sense. If we are not to use common sense then guidelines must become intolerably long trying to manage every situation where common sense might not prevail. 
 ::::::::How do you manage to conclude that people "often" mean Lutjanidae when they search on "snapper"? The numbers are over 100:1 against your conclusion, and suggest they they hardly ever mean Lutjanidae.  
 ::::::::WP:COMMONNAME also says "use the most common name of a person or thing that does not conflict with the names of other people or things". In this case, the fish Lutjanidae is in clear conflict with other fishes also called "snapper". The disambiguation page shows many uses of "snapper" that do not conflict. But when you come to fishes the conflict is clear. I am keen to get this mess cleared up because the conflict between fishes left me confused when I first searched on  snapper. This confusion would not have occurred had I been initially presented with the disambiguation page.