Hearing the characters in the Buffyverse referred to as champions hasn't ever bothered me, because that's pretty much what they all are. Champions defending the weak and helpless and standing against the forces that would harm, subjugate, or even destroy our world, or, in Twilight's case, the entire universe. In a world where there are evil forces more powerful than men, there have to be champions to oppose them, just to preserve the natural order of things. It only makes sense.
And, since you brought up Spike specifically, I don't feel as though I'm getting ENTIRELY away from the original topic (only modesty keeps me from saying that, on the Buffy Boards, I am the undisputed champion thread hijacker of all time) when I mention my personal feelings about the word "champion' as it applies to him. To me, one of the greatest Spuffy moments of the entire series HAS to be when Buffy says to Spike, "It was made to be worn by a Champion," and places the amulet in his hand. From that moment on, I have always seen Spike in exactly that way. The Champion, with a capital "C," distinguishing him from all of the other heroes and champions in the Buffyverse. That was Buffy, in her own way, telling Spike exactly what he had told her the night before: "You're the One." The One who she trusted above all others to never leave her side, to stay the course, to face the end with her, shoulder to shoulder, and spit in Death's eye when it came to collect the world's two greatest defenders. Partners, comrades in arms, warriors to the bitter end. And, lest we forget, lovers, for the simple reason that, just as good and evil must be in balance, so do love and violence.
There are more than one champion in the Buffyverse, just as, now, there are more than one slayer. But, for me, there is only one Slayer and one Champion: Buffy and Spike.
So, no, I don't think that using the term "champion" to describe the characters in the Buffyverse is strange or inappropriate in any way.