The Constitutional purpose of the VP is, of course, as you mentioned, but in a PRACTICAL, political sense, the incumbent party has always used the vice-presidency as a leg-up for the party in the succeeding election.
The Republicans should have had a solid, young conservative like Rick Santorum assume the VP duties around 2005-2006.
Historically, few VPs make it to the presidency. These days, the best past is through a governorship.