It is part economics and part technical conflicts. If you have a huge 5,000 HP motor to pump oil from deep in the ground then 4,160 VAC windings are far cheaper than permanent magnets. I have not heard of permanent magnets being used on motors over 200 HP, but they may exist someday.
Small motors give you lots of options. A universal motor can be AC or DC and reversible. Brushless ball-bearing motors are used when long life is important.
To a large degree the type of power available to use plays a part as well. AC motors with no electronics tend to have low cost and can be brushless if high torque is not needed. If DC power is available then powerful brushless motors are an option if cost is accounted for, else go cheap and use brush type motors.
For cost, which often determines the type of motor used, powerful and expensive permanent magnets are used with a VFD for electric or hybrid cars, as the cost is built into the car. For a disc player it is hard to justify anything but a brush type motor.
An electric hand drill uses a universal motor as it is reversible, runs on AC or DC, and the brushes are made easy to replace. Any other type of motor would cost more and weigh much more.
This answer may not cover all scenarios but should point out the more obvious reasons for choosing one motor type over another, and why some combinations do not make cost or engineering sense.