FDR didn't serve in the military and neither did Woodrow Wilson. They were the presidents during WWII and WWI respectively. Did their lack of military service disqualify them from leading the country into very large wars? While FDR did serve in a civilian capacity as Assistant Secretary of the Navy, that doesn't count as uniformed service. If it did, then you'd have to count Cheney's service as Secretary of Defense from 1989 - 1993 to be honest and consistent.

As for your list, it contains at least a couple errors (perhaps more but I don't have the time nor interest to investigate each name). Ronald Reagan did serve in the military, albeit in a non-combat capacity (like millions of others who served but not in combat). According to this source Dan Quayle served in the journalism unit of the Indiana National Guard (a somewhat similar job that Al Gore performed in Vietnam but not overseas).

Just about every US president has had to send troops into harms way in actions large or small, resulting in many deaths. Quite a few of them had no military experience*. No where in the Constitution is military service a requirement for serving in Congress or in the Executive branch. While I'd prefer it if more members of Congress and the Executive had military experience, that's in line with the US population as a whole. Following WWII, a high percentage of the US population and of Congress had military experience. Today, the percentage of Congress members, the Executive Branch, and of the population as a whole with military experience is reportedly less than 20%.

*According to this source, the following US presidents had no military service experience.

John Adams, Thomas Jefferson (Barbary Pirates), James Madison (War of 1812), John Quincey Adams, Martin Van Buren, James K. Polk (War with Mexico), Millard Fillmore, Grover Cleveland, William Howard Taft, Woodrow Wilson (World War I), Warren G. Harding, Calvin Coolidge, Herbert Hoover, Franklin Roosevelt (WWII), and Bill Clinton.