Fixed lines certainly work, guys, and the ability to do fast extractions should be part of every helo's emergency kit (along with a way to quickly cut those lines, of course.)
The idea that single engine hover is a CAA constraint on a rarely performed emergency operation is an example of over-regulation, for sure. "Sorry mister drowning man, you can't be lifted because you might get hurt if my engine quits while I am hosting you, so just tread water for another half hour!"
Look at the heroic rescue of those folks from the Air Florida crash in Washington DC to realize what a great help a well-flown helo can be in emergencies.
Here is an example of routine fixed string operations - a McGuire rig extraction of an Army Ranger patrol in Vietnam:
The pickup:
The ride home starts:
The site is one maintained by a friend, Mike Gustin, here is the home page, see the photos there, dozens of great ones of helos at work:
http://www.dtroop.com