It's a flyback converter, the winding ratio can be smaller than voltage ratio. There are small off-the-shelf SMPS transformers that can be used, but they are of course still bigger than simple inductor. The switching losses are proportional to peak current multiply flyback voltage, thus much higher with the inductor solution, but possibly still acceptable due to the small output current.
Using a rectifier with voltage multiplication is useful in any case, consider that small storage inductors are often not rated for high voltage.
I would consider a current mode SMPS controller instead of 555 with auxiliary circuitry.