While designated FRS channels have proven to work well some specific applications, such as deconflicting parties in avalanche terrain (as I posted on above) I think a dedicated FRS/GMRS channel for SOS is a poor idea, for most all of the reasons others have listed.
In the front country and side country (AKA "slack country"), these days most SAR calls originate from cell phones. Regarding the use of air-band radios, back in the day, before PLB and InReach, that was a common practice for back country trips in remote areas of Alaska. I recall hearing one story of a party in a remote part of the Brooks Range (which means virtually all of the Brooks Range) who contacted an airliner on an over the pole route, who relayed the request to SAR. These days InReach has almost completely taken over that role. PLBs are also still useful, but the InReach has the huge advantage of allowing reliable 2way comms with the rescue authorities.
In general, for areas without reliable cell coverage, InReach is a much better choice than
any radio for most backcountry emergency situations. They have achieved an extremely good track record for handling SOS situations. For some statistics see:
Learn about the who, what, where, and why people trigger an SOS on their inReach satellite communicator.
www.garmin.com