I think it works like this:
The transistor turns off because the primary resistance is too low to support steady-state transistor saturation. It saturates when power is turned on, due to primary inductance, but as the inductor charges, eventually the collector voltage will start to rise due to the finite beta of the tranny. The positive feedback causes the base current (and voltage) to drop, turning the transistor off.
If the supply were to rise gradually, the lack of DC base current blocking would leave the transistor with Ic=beta*Ib, with no oscillation, which is Audioguru's scenario (I think). With a high beta transistor, the transistor could be destroyed due to overheating in this case.
I also think that the flyback voltage on the collector can be pretty high if the load is light, so care in picking the transistor is needed.
The frequency and output voltage are beta-dependent. It's sort of a minimalist blocking oscillator. Having the frequency determined by an RC time constant is much better unless it's just a one-off, and even then it's not a great idea.
Having said all that, I am no expert on blocking oscillators, so I may be full of crap. Here I am, speculating about the operation of a circuit - just the thing that have complained loudly about when others do it. I did run some sims on it to confirm my suspicions, but I don't think I've ever actually built a blocking oscillator. :roll: