I've just completed giving a couple of Rescue classes, and the points made above are definitely valid - PADI Rescue requires Emergency First Responder or equivalent prior to the first open water session.
Typically people move on to do a rescue course when their focus as a diver moves from dealing with themselves and what they are doing right/wrong to focussing on what's going on around them, and with other divers. ie internal vs external focus.
Reasons to do a Rescue course (regardless of agency) - you'll be a more confident, in control, diver; you'll be much more self-aware in the water; you'll learn how to self-rescue, which in turn will provide confidence in the water.
You'll learn to deal with problems that other divers face; how to manage a situation (which will stand you in good stead in any emergency, not just a diving incident), and how to deal with the details (eg documentation, liability issues).
The physical part of the course helps with skills and putting the various skills together to deal with a rescue situation.
The basic course structure (PADI version) is classroom work, exam, one day confined or open water skill session, one day open water session running through scenarios (where the students don't know what is coming next). They tend to be long days and you will be tired at the end of them.
As for the GF - despite the apparent phsyical disadvantages of being small, rescue classes do take that into account and demonstrate alternative techniques to get the job done. One emphasis in the course is that there is no 'one right way' to perform a rescue. The idea is to learn how to adapt and 'perform the rescue' in whatever way is most effective given the resources/limitations that you have to hand.
Liability - you are under no obligation to perform a rescue, particularly if it puts you in danger. Good Samaritan laws cover a non-professional offering assistance, and it is unlikely that you would be sued, or a suit won against you. DMs and Instructors, if they are acting as such, could be sued and carry professional liability insurance.
Most people I've talked with on the subject tell me that the rescue course is far and away the most fun course to do.
Reasons not to do a Rescue course: .....errrrrr, nope, not seeing any.