Inkjet printer and digital encoder
The printer in your photo uses brushed DC motors, not steppers. You can vary the supply voltage to a DC motor to control its speed, but the actual speed will vary depending on loading so you cannot set the position that way. 

Encoders are required because that is the only way the controller can determine the position of the mechanism. 

DC motors are used rather than steppers because they are faster, more powerful, more efficient and cheaper.