If anything, the system is biased against experience on the national level of politics, especially long-standing senators (who, unlike governors, get pinned down on a hundred Yea-or-Nay votes on visible national issues). Out of the last eight presidents, we've had two VP's inherit the spot, one VP win an election, and five governors.
War and national security being a high-profile issue demands that the candidates give off an aura of toughness and credibility, not to actually have experience in national politics or security. Look at Giuliani.