"Don't need" is highly debatable since even bicycles have gears for the sake of efficiency.
Bicycles are not powered by electric motors, and human legs do not resemble electric motors in any way at all. Human legs have a very limited speed range, just like gasoline engines; that's why transmissions exist.
Imagine driving your ICE car on the freeway in the 3rd gear -- that's going to cause a lot of engine wear and tear due to high engine RPM and drastically reduce mileage.
Electric motors are not like ICEs. Electric motors generate peak torque at stall (that's 0 rpm in case you didn't know). ICEs produce zero torque at stall, and don't even run that way, which is why they have clutches or torque converters, to allow them to idle. ICEs produce peak torque near the top of their speed range, completely the opposite of electric motors.
How many other applications can you think of where electric motors drive something through a transmission (I mean one with multiple gears, not a single-speed gearbox)? There are none. Train locomotives don't, ships don't, they all have direct-drive from their electric motors.
And if you're worried about speed, EVs don't run their motors slower, they run them faster than road speed, using a reduction gear. Go read your own link where that's mentioned. The Roadster only used a 2-speed transmission so they could get away with a smaller (lower torque, lower current) motor, but that really isn't a great idea because the complexity and weight of the transmission negates any cost, efficiency, or space gains you get from using a smaller motor. Higher speeds in an ICE are a problem because there's so many moving parts, and a bunch of them aren't rotating, they're reciprocating (think of the con-rods). This isn't the case in an electric motor, where there's only 1 moving part (aside from the balls in the bearings) and it rotates; higher speeds aren't much of a problem here, within reason.