I don't think anyone's claiming that electric motors can't reach 20K rpm or well beyond that. Or that it's not possible to reduce their speed down to something usable for washing machine purposes. Only that electric motors are available that operate within a very wide range of speeds depending on the application. Why would an application that requires a rotational speed of 1/12th or 1/14th of the motor's output speed be used when much better lower rpm/higher torque candidates are available? And maybe there's a good answer for that, I'm not a washer tech guy. Also, the spin cycle isn't the only consideration. The washing cycle is obviously at a much lower speed, requiring another big reduction for a motor that spins that fast. Also, I'm skeptical that a belt drive system large enough to power a washer tub is capable of holding up to a 20K rpm input speed. That's literally smoking fast, especially on a tiny 1" diameter pulley as you describe.
But if this is a common design feature, it would be very interesting to see documented examples of it in pics and videos. If it is common, then by definition there should be an abundance of easily accessible information available on the net to see.