Back in the day, why did cabinet members get onto Presidential tickets?

[FEMA Camp Administrator]

This is a follow-up to my question about FDR being chosen for Vice-President in 1920. This includes FDR, but is not exclusive to him, the question is:

Why, back in the early to mid twentieth century, did cabinet members get put onto Presidential tickets. I have three, or maybe four examples, and some of the possible reasons:

Deputy Secretary of the Navy FDR for Vice-President in 1920: Because he was a Roosevelt and basically ran the Department of the Navy.

Commerce Secretary Herbert Hoover for President in 1928: Popular?

Secretary of Agriculture Henry Wallace for Vice-President in 1940: shared FDR's ideology?

UN Ambassador Henry Cabot Lodge Jr. for Vice-President in 1960: Nixon wanted to make the debate about  foreign policy rather than domestic policy.

Does anyone else have better reasons for those four examples?

[Southern Senator North Carolina Yankee]

Prominence and influence mostly. In the old days, big players often sought such positions but now, anyone with eyes on the prize often avoid them for fear of being tied to an unpopular administration. If the administration is popular then the Veep is usaully the front runner. So being Secretary of State, or Atty General is basically a career ender now, whereas before they would be top tier Prez candidates.

[minionofmidas]

Complete list of former secretaries of state to later be elected President of the United States:

Thomas Jefferson, James Madison*, James Monroe*, John Quincy Adams*, Martin Van Buren, James Buchanan

where * denotes a direct transition from the one post to the other.

Notice something?

[FEMA Camp Administrator]

Complete list of former secretaries of state to later be elected President of the United States:

Thomas Jefferson, James Madison*, James Monroe*, John Quincy Adams*, Martin Van Buren, James Buchanan

where * denotes a direct transition from the one post to the other.

Notice something?

I'm guessing that the practice stopped because they changed how a Vice-President was chosen, so he would be the natural inheritor of a President's legacy, instead of his Secretary of State.

[True Federalist (진정한 연방 주의자)]

Once upon a time, the Department of State did more than diplomacy.  Over time, those other functions have gotten split off into other departments, leaving a post that has little impact on domestic politics.  The proliferation of cabinet posts also means that each one has less influence and thus less chance to use it as a springboard directly to the Presidency.

[minionofmidas]

Complete list of former secretaries of state to later be elected President of the United States:

Thomas Jefferson, James Madison*, James Monroe*, John Quincy Adams*, Martin Van Buren, James Buchanan

where * denotes a direct transition from the one post to the other.

Notice something?

I'm guessing that the practice stopped because they changed how a Vice-President was chosen, so he would be the natural inheritor of a President's legacy, instead of his Secretary of State.

That was before the election of everyone of these but Jefferson.

This, though, is probably a large part of the answer :

The proliferation of cabinet posts also means that each one has less influence and thus less chance to use it as a springboard directly to the Presidency.

... or even the Vice Presidency, although that still occasionally happens. (Let's not forget Dick Cheney, shall we, though it wasn't directly.)