18s do indeed have more sidewall, there are of course additional "flex" conditions which occur with a taller sidewall, but not all tire-sidewalls are created equal.
For a real 'race tire' it should have a stiff sidewall, you dont want the tire flopping over when you turn the wheel, you don't want the kind of squirm you'd see on a dragster, and they really only achieve those big sidewall wrinkles because of the low tire pressures they run.
For the Emira GT4, I wouldn't say that they run 18s for any 'special' reason that its entirely better from a physics or performance point of view. It could be a GT4 Class limitation on spec tires, it could be for the same reason there are people interested here, that 18's is just a more common size to find performance tires.
I know cars heavier than the Emira run 18s, like GT Classed Nissan GT-Rs. Not sure if everyone is just managing brake temps with better ducting, if the heavier cars are just resigning themselves to having poorer brake performance, HP is also limited in these classes so they dont see as high top speeds to brake from? They throw out rotors after every race because they've absolutely roasted them?
Not sure what the right combination of answers is here. But it does seem they have the stock rear e-brake tucked in under the 18. Honestly, it looks good. (Just looking at the wheel/tire package, not the biggest fan of the wheel design itself) It makes me highly tempted to find a Carbon Ceramic that could work under an 18inch wheel.