Why are high performance electric cars promoted as requiring no gearbox? Moreover, why don't they have gearboxes ("a gearbox" in this context implies a gearbox with multiple selectable gear ratios)?
Some reasoning and my own attempt an an answer:
The statement that "electric cars don't need a gearbox" appears to me as completely wrong, in the context of high performance.
If there should be any consistency to this logic, one might as well say that an electric car doesn't need more than 500 HP either. Why would anyone under normal driving circumstances require 500 HP?
Yet, an electric car such as the Tesla Model 3 or Tesla Model S, which do have around 500 HP, have no gearbox with multiple selectable gear ratios.
It is sometimes said that an electric motor has a "flat torque curve". The reality of this is more complex: https://electronics.stackexchange.com/questions/271674/tesla-car-maximum-torque-at-0-rpm-is-this-correct
However, instead of trying to study that I will just look at a real car's dyno graph.
The following is a dyno graph of a Tesla P100D:
Observe the P-wheel (kW) plot, the actual power the car puts down on the dyno. It reaches a peak at around 3000 RPM, and then gradually it only gets worse.
This is the reality of an electric motor in an actual car. It doesn't have anything close to a "flat curve".
Yes, the total integral of the curve is very impressive compared to a single gear on a traditional car with an engine. However, it does go down, and the summed integrals of multiple gears could probably increase the total area.
As the RPMs increase and the car hits its top speed, the power has become greatly limited compared to the original peak power. At 7500 RPM it only has some 250 kW to offer. This perfectly well explains why all electric cars have a relatively modest top speed when compared to relatively very impressive acceleration figures.
E.g. take a Tesla Model 3 Performance, with its 473 HP (combined) output, with a 162 MPH top speed. Compare this to a 90s factory stock Toyota Supra's 320 HP and 180 MPH top speed. Now, obviously there is a lot more that goes into the top speed of a car, drag coefficient, frontal area, etc. However, this will be true for all electric cars, they all have a low top speed in regard to their respective power outputs.
Even the electric "Rimac C Two" with 1888 HP only achieves a theoretical 258 MPH, compared to the actual 285 MPH of the Agera RS's 1160 HP engine. The Rimac appears to have a two-speed gearbox, but the same question remains why it doesn't have more than two gears. To me it appears to require over 700 HP more to go 30 MPH slower than the Agera. Is the drag coefficient and frontal area that much better on the Agera?
Maybe there exists one or two exceptions? Please point them out. I'm not counting Formula E.
My guess for why a typical high performance electric car doesn't have a gearbox is due to the type of customers that buy electric cars. While a gearbox would give the car a significantly higher top speed, this isn't needed because most customers don't ever test their cars at 200 MPH, and perhaps don't care. However, many do find it exciting to test out fast acceleration at relatively low speeds. This is safer, and is more of a "party trick" that sells. Top speed only sells on paper, for most customers.
Moreover, the car would get more expensive, require more mechanical parts that will fail and require maintenance.
But again, if anyone can claim the car needs more than 500 HP, then with the same reasoning you could also claim it needs a gearbox to exploit that power properly. I don't see why respectable top speed figures aren't important if respectable acceleration figures are.
What am I missing here? Is my reasoning completely flawed?