Brushless DC is NOT the same as 3 phase. Yes there are physical visual similarities like they both have 3 power wires and if you reverse any 2 the motor runs in the opposite direction. But that is where the similarities end.
In a brushless dc motor the rpm is equal to the frequency. So if you were to feed it 60hz you would have 60 rpm. If you need your motor turning 2000 RPM then it would need 2000 Hz no VFD can do this. Some of the controllers are capable of outputting 15,000 Hz or more to get very high RPMs for certain applications. Like a high speed spindle. A VFD WILL let all of the magic blue smoke out of any brushless DC motor.
*** WARNING ***
Semi technical stuff to follow in mt best version of layman's terms.
A brushless DC motor is expecting DC power that is why it has permanent magnets and not inductive. In an AC motor the polarity of the windings and the rotor are flipping back and forth between North and south at the voltage goes back and forth between positive and negative. In the brushless DC the magnets are permanent so they will not switch polarity so as the positive part of the AC cycle starts the motor would try to start spinning in one direction then at the negative part of the cycle came the motor would try to reverse direction. This would give the equivalent of a locked rotor condition.
There are 2 types of brushless DC. There is sensored, witch is what you have and there is sensorless. Sensored is best when starting against a load and/or maintaining a precise RPM. Sensorless is great when there is minimal and/or predictable starting load and precise RPM is not needed.
The brushless DC controller is doing a lot of things that a VFD can not do. In a brushless DC motor it is putting DC power to only one set of windings at a time. The hall effect sensors are looking at the magnets and feeding back to the controller where the rotor is in relation to the coils, The controller can then determine the correct moment to turn off this winding and switch on the next winding. This is especially important during startup to be sure that the correct winding is energized at the correct time.