I don't want to say too much, since I'll probably write at least one more part to explain the background behind this...but I had a few reasons for using Fate instead of Hayate or Yuuno.
Although we don't know the full details, Hayate is already supporting all the Wolkenritter, although she has help from the Tome. Nonetheless, if Hayate dies all the Wolkenritter die, so I'm interpreting that as they
do draw mana from her to some level.
For Yuuno, he's an A-rank mage, but Fate (at that point) is already AAA. So part of the reason why Fate did it was because she just had more raw power, even though she was already supporting Arf.
In story reason, is that it's not entirely legal what they did, and so with only Yuuno to help her, Fate had him do the technical stuff that she didn't know how to do.
Author's reason...well, this came off an idea of mine to explore the moral issues of a potential relationship between master and familiar
.
Wow, didn't think of such longterm issues that could arise, thanks for the ideas!