That's not reaction speed, moreso perception speed.
Does that really matter though? All her troops have 2 lives (which he doesn't know about) leaving him open for attack.
Makima can just simply distract him with a legion of Devil hunters, Hybrids and Devil's. (All of which have regenerative abilities through the consumptionof blood.)
Makima can simply sacrifice a random person and just send him away.
Not Cosmo specifically, but it is in character for Makima to formulate a plan and take down her opponents. She doesn't have to summon Cosmo at the very beginning of the fight, but after gaining some distance and getting an understanding of Gojo's abilities (via reading his mind). He kinda just dies to any of her one-shot moves, heck, he is prone to death by her devil hunter troops who can spawn internal attacks, such as the Mole Devil, which cannot be regenerated (including what Elaj said about verses not being equalized).
She littlerally cannot be caught off guard due to the immense speed difference, not to mention she has auto precognition.
Gojo's only wincon is if he can get a clean purple in and that is if it can erase every single molecule in her body.