[MENTION=12655]Still a Scoobie[/MENTION] has hit the nail on the head.
Buffy is not thinking clearly at this point in time. In fact, I'll bet big money that Buffy KNOWS it's not a conceivable thing that she's asking, she knows it's not a rational request. But she's just found out that the most personal thing in the whole world - her mind - has just been violated against her will, and the minds of everyone she and her parents have ever reasonable come into contact with. She has every right to make that demand, even though she knows it's futile.
Yes, it probably wasn't going to be possible to comply with Buffy's request. Laughably impossible? No, I wouldn't go that far. At this point, I don't think Buffy actually knows that the monk is the last of his order. Plus, monk, it's not like they're a dying breed. There might have been other monks out there that were not of the same order as this one, but who might have been able to carry out Buffy's request, IF she'd gotten the information out of this monk. There might have been monks who knew about Glory and the Key, but didn't actively strive for its protection.
Now, in saying all that, Buffy's request, as we mentioned, was in the heat of the moment, she hadn't thought everything through. I doubt very much that, at this point in time, Buffy would have gone through with her request if she'd been able to had she realized what the outcome would have been.