None of the bard songs or effects require extended singing to get an effect....why is endurance valued over cunning and nimbleness? You have a stronger yell to make someone heal more?
No previous bard incarnation (in either D&D or literary works) valued their endurance over the above two characteristics.
Cunning is not represented by wisdom ... the intelligent bard is
called cunning. Being wise wouldn't normally be considered a bardic trait.
Besides the connection of con to having powerful lungs, a bard can be connected to toughness in that a bard that puts himself into melee fights is not necessarily swift or strong, but fights nonetheless, and is inspiring in that "plucky and tough" way.
The dextrous bard mostly comes out of (a) the 2nd edition subclass of rogue (b) 3x rewarding dex by using it for weapon finesse, ac, ranged attack spells, etc.
Bard as a rogue variant means he needs dex. However, a bard doesn't necessarily need to be a rogue variant ... he has the intelligence and charisma of a roguish type, but he doesn't necessarily need to be an acrobat or a sneak or a theif. He is a storyteller, musician and deals in magic that fogs the mind and lifts the heart. And to tell stories of great battles and heroics ... you need to survive, so the traits that makes one a survivor, like toughness, are important as well.
EDIT:
Ultimately though, the bard isn't inspiring with CON. His primary stat is charisma, it is what inspires. However, he relies on secondary stats, either his wits (int) or his toughness (con) to keep him and his friends alive.
