Running bldc motor without hall effect sensor or back emf
A 3-phase BLDC motor can be operated open-loop as a permanent-magnet synchronous motor (PMSM). If the motor is started at a low frequency and accelerated at a controlled rate by limiting the rate of frequency change, it can be operated over a reasonably wide speed range. The applied voltage must be adjusted to maintain a relatively constant ratio of voltage to frequency. This is the basic method of variable frequency drive (VFD) control used for induction motors. Maintaining the V/Hz ratio, even open-loop, can keep the motor from being "hopelessly inefficient" as @Brian Drummond put it. It will also allow the motor to develop full torque over a useful speed range. An open-loop VFD controlled PMSM will not have high starting torque or the ability to cope with rapid load changes. It could also experience torque-angle oscillations if the load inertia is too high.

I believe it would be fair to say that the emf and hall-effect feedback techniques provide everything that V/Hz control can do plus the things that it can't do. However I believe that sensorless-vector VFD control techniques can provide most if not all of the dynamic performance and perhaps more torque for a given size motor and higher efficiency. The controller cost and complexity may be higher with the VFD approach.