Tetsujin, you are wrong.
Buffy died in Season 1: Prophecy Girl.
Why?
They didn't know the show had gotten renewed. It was a 12 episode season filler. Buffy died. That was it. Slayers have been around before and will be around. Slayers in Training. All seasons reflected this (down to the primeval slayer and the cuurent seasons Slayers In Training dying).
Now, when they revived her (Angel couldn't vampires cant breathe according to season 1), She was dead for a few minutes, thus activating, Kendra, a by-the-book-Slayer. As Willow put it, a 'She-Giles'. Buffy even said earlier that she never saw a Slayers Handbook, yet we find out in Season 2 "Whats My Line Pt 1" there is, indeed, a Slayers Handbook ("Wouldn't it be cool if they had a shirt too?").
Now, Kendra died in Season 2 "Becoming Pt 1" which activated Faith. Buffy died in Season 5 BUT since she had already died in Season 1, she couldn't activate another Slayer. Why?
Faith is the TRUE technical current slayer. The council knows Faith is evil and Buffy has survived longer than any other slayer so therefore, the council backs her up, even though they despise it and her lack of training.
We havent seen Faith or Kendra use 'Demon sensing' so thats why i am a little questionable on it. Thats all. But if it works, go for it =)
*puts on his "Im-A-Slayer-Ask-Me-How" Button