Should There Be a Minimum Required Qualifications for the Office of President

The US Constitution only gives two qualifications for the office of President of the United States.  First, a person must be 35 years of age.  And second, the president must be a natural born citizen, meaning a citizen by birth.

I think  after this election, both major parties should consider minimum qualifications before accepting just anyone to run for office.  This election, especially for the republicans, the nomination process has become a disaster.  Here is my suggestion.

A person wishing to win the nomination for the presidency from either the Republican or Democratic Party, please consider these as the minimum qualifications.  In history, you will notice that very few men who have run for the office have done well without meeting one of these qualifications.

1.  Achieved the rank of Major General in the Armed Forces, or it's equivalent.  And has commanded troops during a major war.  Examples: George Washington, Zachary Taylor, Ulysses S. Grant, Dwight D. Eisenhower, Andrew Jackson

2.  Served at least one term as the Vice President of the United States.  Examples: John Adams, Calvin Coolidge, Richard Nixon, George H.W. Bush, Martin Van Buren, Thomas Jefferson

3.  Served at least one term as the Governor of a State.  Examples: George W. Bush, Bill Clinton, Ronald Reagan, Jimmy Carter, Franklin D. Roosevelt, Woodrow Wilson, William McKinley, Rutherford B. Hayes, James K. Polk

4.  Served at least one term in the United States Senate.  Examples: John F. Kennedy, Warren G. Harding, Benjamin Harrison, Franklin Pierce, (Some who have served partial terms in the Senate have been elected: Barack Obama, William Henry Harrison, Andrew Jackson.  Except for Obama, the others had other experience, mainly military experience, to make up for lack of time in the Senate.)

5.  Served at least one term in the United States House of Representatives.  Examples: James A Garfield, Abraham Lincoln, William Henry Harrison

6.  Served at least one term as a cabinet-level Secretary in a Presidential Administration: Examples: Herbert Hoover, William Howard Taft, James Buchanan, John Q. Adams, James Monroe, James Madison

7.  Served at least 4 years as an associate justice, or the Chief Justice of the US Supreme Court.  However, no one has ever been elected with this experience.

8.  Served as the Mayor of the hub city of a Major Metropolitan Area.  However, no one has ever been elected with this experience.

All of the Democratic Candidates have one of these qualifications except for Lawrence Lessig.

Here are the Republican Candidates who have failed to meet these qualifications

Donald Trump
Carly Fiorina
Ben Carson
Mark Everson
Andy Martin

And here are those who have served partial terms in the Senate

Ted Cruz
Rand Paul
Marco Rubio

However, assuming they would have finished to taking the oath of office, Rand Paul and Marco Rubio would have completed 6 years in the senate.

Would this have cleared up matters?  On the GOP side you would have been left with

John Kasich
Mike Huckabee
Rick Santorum
Jim Gilmore
Jeb Bush
Bobby Jindal
Lindsey Graham
George Pataki
Rick Perry
Scott Walker