Why sacrificing your main pawn which was nicely on track weakening tne white council? Why not make it stronger so it could weaken the Sidhe courts as well? For example by providing it with a better ally by removing the current white court leadership and if that fails making room for the Fomor to take their place?
I don't see Cowl's main objective as weakening the White Council. I see it as weakening all the supernatural powers, Red Court, White Council, Faerie, everyone. The Red King and the LoONs don't exactly look like pushovers (unless like Harry you actually take the Red King's crazy act in Changes, which conveniently goes away the instant it is no longer useful, at face value.) Making the White Council too weak relative to the Red Court just leaves the Reds free to disengage much of their force; the situation where the White Council and the Reds both get beaten down but are still engaged works better.
I also see no reason to think Cowl's long-term goal is to obliterate the leadership of the White Court, rather than that being a fallback; without Harry interfering, a White Court shift of policy towards drawing them into war with the White Council looks much more likely to come of that meeting in the Raith Deeps.
In this context it is easy to see why Mab and Odin wanted the red court gone.
That is providing a answer for a non-existent question, IMO. The Reds made a peace offer, under the terms of the Accords, at the start of Changes, without the intent to keep it. That is grounds enough for Mab to want them exterminated; they are
her Accords, and the Reds had PG as a warning already.