The "next in line" thing is just a factor of selective history reading really.
In 1984 and 2000 the first elections they could, Democrats went with their last VP. Lieberman was a bit of a curve ball. But had Obama not run Edwards was polling as the primary threat to Hillary.
Reagan made himself "next in line" by nearly beating Ford, then Bush was his VP. Dole is where the "next in line" theory got traction, but W. Bush thwarts that. (I'd argue Colin Powell was the true "next in line" for both 1996 and 2000. Plus go on CSPAN's site and watch the early 1996 debates.

Bob Dornan and Morey Taylor

)
Prior to this you had VP Humphrey getting the Dem nom in 1968, and Goldwater/Nixon (Romney in part) both derailing Rockefeller front-runner bids.
The McGovern and Carter paths to the nomination are quite interesting. McGovern basically designed the primary system and even into 1980 a lot of candidates were running the "wait until the convention" campaign style but he knew he could rely, like the Paulites, on people who did know the rules becoming delegates first and upsetting the balance. Then Carter's team had projected that campaigning (he started in 1974!) and winning early, even if insignificant technically would help get the resources for the needed infrastructure that ended the late candidacies that Jerry Brown, Frank Church and some others attempted in that same campaign.
Plus, Ted Kennedy was the real front-runner in both instances and would have been in an open 1980 or 1984 I think.
I think both McCain and Romney's nominations like Dole and Kerry's had more to do with "these are the other choices?" When nobody else seriously threatened them in early states, they rolled quickly.