It's interesting. There's several reasons.
This was a period in which Republicans dominated the White House so there were less opportunities for Democrats to use roles in presidential cabinets as a platform to run for President.
Democrats developed a tendency to go for new faces like JFK, McGovern, Jimmy Carter, Bill Clinton and Barack Obama. That skews young. It also led to Gore being fairly young when he was a two-term Veep.
Republicans developed a liking for politicians who were outside politics before running for higher office. This meant they had to be accomplished and it takes a while for that to happen. Eisenhower was in his 60s during his first bid for office. Ronald Reagan became Governor at 55. George HW Bush became Congressman at a relative young 43, but it took him a while to build a sufficient resume to run for Prez in 1980 (which led to him getting the nomination in 1988.) George W Bush became Governor at 48. Mitt Romney became Governor at 54.
A very significant factor I just realized is that Democrats have a strong tendency to pick people who got into politics at a relatively young age. JFK was a Congressman at 29. LBJ was a Congressman at 28. Even Nixon, a historically young Republican nominee, was 33 when he became a Congressman.
Humphrey was 34 when he became Mayor. McGovern was 34 when he became Congressman. Carter was 38 when he became a state senator. Mondale was 31 when he became Minnesota Attorney General. Bill Clinton was 30 when elected Attorney General of Arkannsas, having failed a congressional bid two years earlier. Al Gore became a congressman at 28. John Kerry ran for Congress at 28. Obama became a state senator at 35.
I think it is a very good explanation. It makes sense that the most pro-business party has leaders who were businessmen before becoming politicians. And if they were businessmen, they could not start being politicians very early.
Chalenging an incumbent has no much relation to being youger, because in four of the last five elections, the candidate of the party trying to pick the White House was older than the candidate of the party trying to hold the White House.