Why can't I change the speed of an ininduction motor by changing the voltage?
The issue with controlling ONLY the voltage is mostly of torque and load. An AC asynchronous motor will lose torque proportional to the voltage reduction, but also lose PEAK torque at the SQUARE of the voltage reduction. Peak torque, typically around 200% of Full Load Torque, is what the motor utilizes to maintain speed as load changes. So if you cut that down by the square of the voltage change, your motor becomes less able to react to any change in load. The result is an increase in slip (not a decrease) and when slip increases, the motor draws more current, but in this case without producing enough torque to get back to design speed, so it overloads and possibly stalls.
IF however, the LOAD is reduced at the same time, the motor may run fine. For example if the load is a centrifugal (quadratic) machine like a pump or fan, lowering the voltage and dropping the torque results in a lower speed. But in that type of load, the load on the motor drops at the CUBE of the speed change, so the pump/fan couples less with the load and it might run like that. But notice that the torque drops at the square of the VOLTAGE, and the load drops at the cube of the SPEED, they are not the same thing and the complex dynamics makes this a very tricky situation to control accurately, then if anything in the load changes, the motor may not be able to deliver more torque and stall.
May people try to take advantage of the Wye-Delta motor wiring issue you mentioned, by purposely leaving the motor in Wye, which effectively applies 58% voltage to the windings. This reduces the running torque to 58%, but reduces the PEAK torque to 33% (.58 squared). 33% of the 200% peak torque is 66% of FLT. So the running torque is 58% of FLT, but the ACCELERATING torque is only 66% of FLT and the motor can be easily stalled if there is any change in the load.