Is it really so hard to believe that after 300 years of that, the future idea of what their military should be would be somewhat different than ours?
Somewhat different like leaving your capital undefended, even through you have the obvious capacity to defend it? Even during times of war, a sizable portion of the British navy was kept in home waters.
So different that when the Captain of your newest flagship is disabled, you don't simply reassign a experienced captain or first officer from the fleet in the Laurentian system to take command? When Captain Honors of the (real) USS Enterprise was fired this past January, the US Navy installed Captain Mewbourne, chief of staff for Cyber Command. They didn't give command of the USS Enterpise to a third year cadet.
People apparently are having issues accepting the premise that things change.
Well certainly trouble accepting that things change to the point that they wouldn't work. You don't design your defenses around requiring a "miracle save" whenever your capital is attacked.
Of course, numerous people will oppose this because they 'need' something to 'relate to'.
Would that "something" be the reality of their own life experiences and thousands of years of history as to what actual works?
(incidentally ... money work)
If the United States was invaded today, how many of our troops would be in the U.S. ready to go into battle on the beaches within a week?
Of the one and a quarter million people in the active US military, one million are in the "lower forty-eight." forty thousand are in Hawaii, twenty thousand in Alaska. The remainder are out of county. So to answer your question ...
most.
Plus, reserves, guard, militias, police, and the most heavily armed civilian population in the world.
how many people on a space shuttle mission would be considered "enlisted"
The shuttle is basically a high flying plane, however the mission commander and the shuttle pilot are the "officers" (usually actually are), and the various mission specialists would be the "enlisted," in terms of division of command authority.
Could a U.S. Naval captain decide today to randomly invade ...
Depending on his (hers) mission orders and rules of engagement, yes they might have that discretion. Certainly to enter another countries air space, or territorial waters. Even land troops on foreign soil by their own orders (say a aircrew was down) without needing to check "upstairs".
and a substantial part of their officer corps.
If you lose ten percent of your ships with all their officers, the ratio of officers to ships increases, because in any (modern admittedly) service, the majority of your officers aren't on ships at any given time. The fleet being decimated over Vulcan would have made it less likely that Kirk would have gotten a command, not increased it.
