Why is the spiral of an electric kettle made from a conductor with a large cross-sectional area?

According to the Joule-Lenz law:
Q = I ^ 2Rt, but since the kettle is connected to the electrical network in parallel, we use the formula:
Q = U ^ 2t / R.
This means that in order to increase the amount of heat released by the spiral, it is necessary to reduce the resistance (Q ~ 1 / R). The resistance is found by the formula: R = pl / S, where S is the cross-sectional area. This means that in order to reduce the resistance, it is necessary to increase the area (R ~ 1 / S). And it turns out that the larger the area, the greater the amount of heat released by the spiral (Q ~ S).