That's a curious statement. What's necessary for performance then? What kind of performance?
Maximum cornering forces are mostly related to the rubber compound, the placement of the rubber on the surface during cornering (i.e.: the alignment) and weight transfer. Excessive sidewall can impact the placement of the rubber, but other approaches can reduce that impact. (Stiffer sidewalls, rounder shoulder on the tire, high amounts of negative camber[1], etc).
Maximum acceleration is a function of power to weight, including rotating mass. Reduced moment of inertia in the tires will lead to faster acceleration times. Smaller wheels typically have lower moments of inertia, but carbon-fiber wheels might manage to be lighter than rubber.
Maximum deceleration is mostly a function of grip (see cornering, except negative camber hurts you here: you want the tire to be flat while braking) and the ability of the brake surfaces to dump heat. Bigger rotors have an easier time dumping heat, and this is the first place where larger wheels are a material benefit: they allow space for larger rotors. Similar to the other elements, it can be compensated for in other ways, but it's quite hard to compensate for in a way that's cheap (carbon ceramics fail here) and works at a wide temperature range (race pads fail to work well when cold).
The remaining argument for minimal sidewalls is when entering the corner or switching between corners. Smaller sidewalls tend to make it easier to have the car setup for the next corner.
It's been way too long since I last read it, so I might be thinking of the wrong book, but I recommend "Going Faster" by Carl Lopez. If it's the book I think it is, it goes into a ton of detail about how weight transfer and alignment settings impact cornering speeds.
TLDR; most track-dogs I know tend toward the smallest wheel option that fits over the largest brakes, when given the choice. An inability to properly change the alignment may affect this decision, but I understand there are products for that.
[1] my understanding is that you can't really dial in a ton of negative camber with the stock setup?
