The Cage may represent the tiniest portion of the IP, but it also represents the only portion of the IP that was never touched by NBC's changes. It featured an ensemble cast (a staple of later series, and even late TOS), and a focus on exploration and peaceful resolutions over fighting. A vast majority of TOS episodes are resolved peacefully, very few are the enemies "killed." Want another example? Devil in the Dark, where the Horta turns out to be a protective mother. A Piece of the Action, where Kirk turns himself into a "Boss" to bring peace to a world of Gangsters. The Trouble with Tribbles, which arguably should've turned into a shoot out between the Klingons and Federation.
So few Star Trek episodes were solved with violence. In most episodes violence tended to complicate matters. The crew of the Enterprise was willing to fight if necessary (Balance of Terror is an excellent "fight" episode), but would attempt any other option first, and that was first shown in "The Cage" (rather than "Where No Man has gone Before" which ultimately was a "fight" episode). The Cage is Trek at it's purest, and when you boil down the Original Series, you see that it ultimately boils down to the Cage as well, just bogged down in some places. TNG was similar in that it's essence was not fighting, but peace.
Voyager and DS9 were great series, and Voyager is far and away one of my favorites (probably just behind TOS), but both failed to focus on the peace over war concept. Arguably DS9's war was inevitable, and represents the part of the Federation that's willing to fight when forced, but Voyager really became a Voyager vs the Borg, which was cool but wasn't the pure Trek of TOS or even TNG. Voyager had an excuse too, in that they were trapped and weren't really representing the Federation specifically, and even then managed to promote peace in many episodes (I think the one called "Void" is a good example, but I can't really recall the name). Enterprise threw all explanations away and focused on action and fighting in many episodes. They really didn't get back to the whole "Peace over Fighting" concept until the final season.