The most fun way to understand the benefits of this in my opinion is to check out how crazy powerful and surprising software digital synthesizers and effects can sound and then think about how offloading any kind of digital synthesis/processing to analog means is free computing cycles from the digital perspective.

If you tried to capture the surface of a swimming pool along with measurements of momentum and then use a digital algorithm to predict how the surface will fluctuate (assuming no further disturbances beyond boundary conditions) it would be very quickly a computationally overwhelming task... but a real swimming pool just keeps on doing it endlessly.