Season 5 was originally the end of the series, so the end had to be final.
Buffy jumping off the tower, Buffy being told what her gift would be by the 1st slayer.
The wording of what the slayers gift is..... those words were specific to the slayers creed, not to an individual action.
I'd suggest the writers knew how to write in English, those words were chosen to be in that order. They were specific to the ending, effective and powerful.
The action of jumping off the tower, how to end a series? Oh, imagine the dramatical impact!
The slayer lets her sister jump to her death, or when put another way. The Monks of Dagon entrusted the slayer to protect the key, and the slayer let the key/ Dawn jump to her death? Really? Is that how the slayer should be remembered?
Another tv station took on the rights and season 6 and 7 happened, but that should not distract you from the fact that the end of season 5 was to be the end.