A quick look around my apartment shows a bunch of appliances powered by universal motors: drill, vacuum, blender, and probably several more. What makes the universal motor such a popular choice in small appliances? I'm guessing it has nothing to do with the ability to run on both AC and DC, since none of these devices work on DC and 120V batteries are rare.
Universal motors have a low manufacturing cost for the high quantity manufacturers. When the load increases, they slow down and develop more torque without drawing disproportionally high current. They are inefficient, but that doesn't matter very much for things like food mixers and blenders or small power tools that don't require much power and are generally used only occasionally for short periods of time.
With universal motors, variable speed can be implemented inexpensively inside the appliance in a small space.
Permanent-magnet DC motors are more efficient and thus better for battery operation in terms of longer operation between charges. They are used in cordless power tools and appliances. Those that I have examined don't use the most expensive types of magnets.
We may see electronically controlled permanent-magnet motors take over more of the small appliance applications as manufacturers reduce the manufacturing cost for that technology. The Dysan "digital" vacuum cleaner motor is an electronically controlled permanent magnet motor.
Expanded in response to comment: Universal motors can easily operate at higher speeds than induction motors. That is particularly useful for vacuum cleaners and blenders. When operated from domestic utility power, an induction motor is limited to RPM = 120 X f / p where f is frequency, either 50 or 60 Hz and p is the number of poles, minimum of 2 (or 1 pair). That means that in induction motor can operate at no more than 3000 or 3600 RPM. It is not difficult to exceed for a small universal motor to exceed that. The speed of a small universal motor can be as high as 15,000 to 20,000 RPM.
Universal motors are lightweight, have a high starting torque, and can run at variable speeds.
Shaded-pole motors are lightweight, have a low starting torque, and require additional hardware to run at variable speed.
Large induction motors are heavy, have a high starting torque, and require additional hardware to run at variable speed. They are also expensive.