The last two Vice-Presidents were from two states with the minimum allocation (3) of electoral votes -- Wyoming (Cheney) and Delaware (Biden). Neither was from a state that anyone thought in doubt in the Presidential election.
Dubya chose Cheney for his alleged skills as an administrator.
Obama chose Biden because Biden was the poorest Democrat in the Senate -- someone with no possibility of any scandals for personal gain.
Thune? What does he have to offer?
Thune is a "safe" pick; he won't make mistakes and he's fairly well vetted. He "looks" Presidential, and he's acceptable to the whole of the GOP.
Thune may be boring, but he's not the kind of guy who'll be the World's Loosest Cannon. He'll be message-disciplined and if he doesn't help a whole lot, he won't do any harm.
That's the same rationale that led to Paul Ryan getting the VP nomination.