Why there is no brushless field wound DC motor
First, not all brushless motors use permanent magnets (PM). Some are switched-reluctance, e.g stepper motors, or induction motors, particularly large polyphase motors. BTW, one characteristic of PM steppers is that they can be self-locking or cogging, acting as if a detent keeps the armature in position.  

Second, it's a matter of definition. A shunt-wound motor uses the same power source in parallel for the field and armature, using a mechanical commutator. Replace the commutator with a Hall-effect sensor and electronic switch and it's a brushless motor, but the term "shunt-wound" is not applied. They're still the same basic design, though.