That may have been what the founders envisioned, but in the modern age the most important criterion for a VP candidate is helping the President get elected.
Historically that was why many Vice Presidential candidates were from swing states, to help the ticket win. The Democrats sometimes had a Southerner on the ticket (no Southerners as the Presidential nominee after Polk until LBJ unless you count Wilson, who was Governor of NJ when nominated, or Truman, who was the incumbent in 1948). FDR had Garner from Texas. Adlai Stevenson had Sparkman and Kefauver.