You are correct about fan blade out and continued run-on power requirement. That is a requirement for the bird ingestion test.
The run-on power requirement comes from the frequency of multiple engine events. Anything to do with the environment you fly in presumes multiple engine involvement Rain/hail inlet ice, flocking birds and maybe someday volcanic ash.
The bird requirement gets a little complicated since it presumes an air-turn-back with a missed approach (contaminated runway etc.) and the need to do a go-arround. I don't recall anybody doing one of these on the newer engines certified to this standard. A couple of events with older engines which were definitely high pucker factors