Analog circuits still have finite bandwidth and rise/response times. The engineering trade-offs are more complicated than the gp presents.
The big but mixed advantage of an analog control loop or signal processing chain is "no software".
There's no real reason to do simulations on an analog computer today, though I think using one for model-in-the-loop would be fun, and somebody is probably doing it somewhere.
Some people are building analog chip startups today because there are reasons to do analog computation. Among the applications are low-precision high-speed parallel math, neural networks, and image and audio processing.
The big but mixed advantage of an analog control loop or signal processing chain is "no software".
There's no real reason to do simulations on an analog computer today, though I think using one for model-in-the-loop would be fun, and somebody is probably doing it somewhere.