I also found the opamp regulating it's own supply in the Horowitz/Hill. It is nothing like my circuit. And i did come up with a reasonable explanation why my circuit does work. I will save that for later, cause i have now a huge cold.
Ignoring your circuit and exact/specific details, to make it easier for me to explain.
So in general.
The Op-amp would need to produce a voltage (at its output), potentially a bit above (depending on the exact circuit), the supply voltage. This is completely impossible.
You have got the diode base/emitter junction (of the transistor), to attempt to lower that voltage requirement, by about 600/700mV. But it is still a very bad idea. I'm not even sure it would work, let alone be a robust and reliable technique.
Any overshoot, interference, high voltage interference on the incoming mains (which sometimes briefly can partly get through, to an extent), would immediately break the datasheet. E.g. Maximum input voltage, common mode range, etc etc . Depending on the exact datasheet op-amp model.
Exceeding the common mode range, and/or other parameters, may latch up, damage or other undesirable effects, could occur.
Once your circuit were to ever exceed the max output voltage of the op-amp plus a few hundred millivolts or so. It appears that the transistor, would "latch up", and permanently be energised (by the too low voltage on the output of the op-amp).
I.e. Although the op-amp is rail to rail, it still has datasheet limitations. Such as voltage drops, when any current is flowing, lack of ability to exceed the positive supply terminal, and max voltage limits, which attempting to exceed, would break the datasheet rules and potentially not work either.
I can see much worse technical problems, which would be likely to stop it from working correctly, but would take ages to explain.
There is tons more I could explain what is wrong with that type of idea, but I will stop now.
To give a quick counter point, to my own stuff above.
It is true that some major, manufactured items, have taken various short cuts (at times), in their electronics. With all manor of "crazy", but actually it works, ideas.
But to end. I would strongly recommend that internal power supplies, for your electronics, is done in a robust, reliable, tried and tested way. By and large there is no need to try wild stuff.
Sometimes clever electronics can be made by exploiting electronics stuff, in unusual ways. (Outside of critical bits, such as internal PSU's)
But I would still recommend that the internal power supply, is done in a somewhat regular way.
tl;dr
Any issues/noise/surges/faults/unreliability in your internal power supplies, will usually/often ruin the project. I.e. It won't work properly.
Just because something works (I'm not sure if that would even be the case), and is almost within the datasheet specifications (I doubt it, without doing a huge analysis job). Does not mean that it is a good idea.
If you are determined to do it. Then why not do it with a separate op-amp (high voltage), which is powered off the incoming voltage.
Get well soon!