The trend is towards DC motors that are electromechanically AC motors, but supplied with AC current generated by an inverter from a DC power source. The inverter can control the motor more precisely than a fixed-frequency grid voltage can, and the DC source can be supplied by a battery.
In terms of reliability, the inverter is still an extra part that can fail, but on the other hand, it's also much less likely to blow a fuse when your motor shaft stalls on startup.
Yes but they work on feedback (if the washing machine has 5kg load, use frequency X, voltage Y, if machine has 10kg load ... they don't measure the load they measure how the motor reacts to their first guess voltage (this is called startup) and then adjust). Even comes with mechanical advantages: instead of using brakes, you just use the same motor and reverse the feedback.
Now if you want the ability to adjust frequency and voltage, at large power levels, you're talking about changing the parameters of an inverter. So what it's going to do with AC input voltage is AC -> DC -> AC* (* with different frequency and voltage, synchronized to the rotation angle changes of the drum of your washing machine). This comes with a second advantage: it's easier (and cheaper) to be tolerant to frequency and voltage changes in the wall plug, maybe even tolerant enough to have one device that works in US and EU (and ...)
You're doing this because the power plant is not going to change frequency or voltage based on how fast your washing machine is turning, but doing that makes the washing machine much more efficient.
In terms of reliability, the inverter is still an extra part that can fail, but on the other hand, it's also much less likely to blow a fuse when your motor shaft stalls on startup.