One part of the answer is that the circuit does does not really need a that much faster opamp.
Here is a
link to the lastest, modified version. The author has recently
measured his power supply. Switching a (FET) load from 0.3 to 1 Amp at 300Hz takes 20 micro seconds to regulate. Others have confirmed these values.
Ok... admittedly using a TL071 but still not to shabby for a not much newer old op-amp.
A less obvious part of the answer are the involved voltages.
This is old(er than me) analog tech. Most of todays op-amps do not survive Voltages in the 30V region.
(This modified version has been a bit defanged, it it uses different voltages in the voltage regulation than the original.)
Back to topic:
The important "trick" and reason for the fast response time in this form of circuit is that the ground of the op-amp rails and the and reference voltage
float on the positive output voltage. This way you always have the full regulation output at the base of the power transistor(s). That is why the op-amps and reference voltage have their own transformer.
Several Gossen Konstanter, Several Anatek power supplies, HP/Agilent E361xA, E3630A, E6236, Leader LPS 151&152 - all use the same principle.
There is also a HP Appnote, No.90 from 1967 on this topic, it was base for the development and publishing of the circuit in 1973.
There are some later clones that use the negative output as reference. They are much worse because you now need a much higher voltage difference - even worse, depended on the output voltage- to regulate the system. In comparison a quite obviously stupid idea.
The mentioned dual power supplies the ground for the op-amps floats on the (middle?) ground of the output. A contradiction? No, look where the power transistors are in that case.
If I'll manage to get this thing build I'll post a bit more about it.