I'd like to toss my two cents in here, because I think the idea is actually kind of neat.
The Fate series has a really interesting variety of Magecraft, etc in it, and if you've seen Apocrypha (which most people seem to loathe) you'd find that experienced Masters are actually pretty damn fun to watch fight. Heck, Kairi (Saber of Red's Master) actively participates in the battles, so he's not really dead weight at all.
I think playing as a Master could potentially be a lot of fun, with a lot of development for their personalities and their skill sets. It's all about your perspective, I'd wager.

Though I do think not being able to play a Servant could gimp the idea considering most people want to jump in right off the bat with that.
From my understanding, every roleplayer is working for the same one of the five factions, trying to eliminate the other factions (and the NPC parties they employ)? Basically a HGW but with a Servant split between a group of Masters instead of only a single Master?

I think the biggest obstacle is letting players play as Servants. As [@KoL] said, it's kind of the biggest thing that attracts people to the Fate roleplays. That being said, you could totally delegate a Servant to a person entirely separate from the people playing the Masters in order to keep them from being dragged around by a single person.
That said, though, the issue of people going off and walking around is going to be there regardless. You could totally enforce some sort of buddy system that demands that the Masters all travel together to make any retaliation either impossible or an even fight, which I think could lead to a sweet moment when the traitor finally decides to go turncoat and turn the odds from 5v5 to 6v4.
Oof. I'm kinda excited for this lmao.

That said, I'll refer to Apocrypha again in that I personally think they had a decent setup. Keeping the factions so the players don't have a reason to go at each other (except the traitor) while also giving them a sort of hub to stick around, but then also allowing each player to have their own Servant/the single Servant depending on whatever you want.

These are just ideas, but I like the idea of having the battles focus a little more on a Master, since the stakes are so much higher and they're arguably the more important in the Master-Servant relationship.
I think it'd be fun to narrowly escape an assassination attempt by an enemy [s]Stand[/s] Servant as a Master, only to summon your own Servant at the last minute and turn the tables.

This is just me rambling like an idiot, though, so I'm sorry if I'm being overbearing or being silly~
I like this idea, though, so I'd like to help iron out the problems so it can succeed.