...Kana handles the Servants and deals with their drama when she isn't planning for the next Singularity.
Thought of this a bit late, but... Considering what we've been shown, most of the work in actually defusing the Servant-induced incidents is actually being done by Ritsuka (even if it's just "call in Herc as an impromptu enforcer"); Kana, meanwhile, seems to either ignore problems that do not completely jeopardize Chaldea or encourage them to misbehave, which just stresses Ritsuka out even more.
Basically: Show, don't tell; if we don't see Kana defusing situations, we won't believe she's doing that. The "Ritsuka does all the work while Kana goofs off" comment has a point, in that we have never seen her do anything else when she's not in a Singularity. It doesn't help that she spends an unspecified percentage of her time trapped in the Gate of Babylon, and thus completely incapable of doing anything. In fact, as far as I'm aware, the ONLY time she's done the job you stated she performs was when Stheno was summoned, and that was solely because Ritsuka was rendered incapable of acting as a Master by his own Servant (who had, additionally, explicitly stated that she would not restore him purely due to her own ego). Beyond that, she seems to be more of an instigator.
She's gonna have to shape up outside the Singularities to shake off the "Kana is a liability" reputation, I feel. Of course, I might be going overboard (like I did with Kiyo and said I would with the Summer Servants if I let myself get started on them), and I wouldn't be surprised if I'm forgetting something, but I'm just telling it how I see it, and the way I see it is that it's time for Kana to be the butt of the "unruly Servants" running gag.