As far as people are concerned, human nature doesn't change; only technology changes. And that's why, even though both Shakespeare and Gilbert wrote for their own eras, both writers are still valid/interesting today.
The wonderful thing about Gilbert's satire, is that he chose themes that have not only held up, throughout the ensuing century plus decades, but many have become relevant as people have come back to the same things again and again...transendentalism, aethetics,"feministism"/women in college, class warfare, do nothing pols, stupid laws, "the Peter Principle" stuff, etc. !
The song does not say which George, but it does feature the Battle of Waterloo, during which George III was king. However, I agree that he does not deserve credit for Wellington's victory. In fact, in his later years he suffered from dementia. See the movie The Madness of King George. Henry V was actually present at Agincourt, but later monarchs get too much credit for their military forces' triumphs.