Yes, Buffy is much more than just a teen slaying vampires. Notably, in the first season, there were many episodes where a vampire was nowhere to be seen... this was corrected in season 2 onwards, with at least one vamp-killing scene for a show with "vampire slayer" in the title.
Buffy as a whole was about the transition from high school to adult-hood (really underscored when Joyce died and Giles left for England... the adults gone with the kids having to become the adults).
Now, here's something I'd like to explore. The episode "Lineage" had something very, very powerful in it. Wesley's "father" shows up (a cyborg, really, but no one knows that until the end). Brings out all the daddy-issues. Well, at the end, "Roger" (the cyborg) is trying to get away with some artifact that robs Angel of his free will. Wesley is trying to talk him out of it. Then "Roger" grabs Fred, and Wesley shoots without hesitation, until he's out of bullets. He then throws up, thinking he killed his father, and then sees the glamour wear off, revealing a cyborg.
Here's the part that makes it even more powerful, to me. Fred is trying to console Wes later, saying "part of you knew it wasn't him." He replies (paraphrased):
"I was sure it was him." (It might be a direct quote, I dunno...)
To me, it's more than just the fact he thought Fred was in danger. Sure, he loves Fred... I don't think he loves his father all that much. Inidcations have been that Roger was a very belittling man, and the source of Wes's insecurity. Grabbing Fred was the "final straw", and he took out all his rage on his father at that moment, shooting him until he was out of bullets.
Anyone else get a lump in their throat from that episode?