What’s called aerial silk is not made of nylon, not silk. There are different kinds of aerial silks available, depending on how stretchy you want it to be, whether it should be fire-proof, etc.
Aerial yoga is indeed popular, using the same fabric aerialist artists use.

I’ve used similar fabric for comfortable inverted suspensions, and it’s quite nice, especially when used instead of a hip/waist rope – a rope can still be added on top for visual effect, but the model’s weight was supported by the fabric.

The only occurrence of suspending someone with real silk ribbons I saw was several years ago in London, performed by the Leather Family at one of the LAMs; it was quite safe as silk is very strong, but it was painful for the model, as the ribbons were cutting into the skin – it was a short suspension, so it was bearable, but just.