Regarding the emergency services sending a link and the location being sent back to them. A system achieving this is successfully in use by UK Mountain Rescue (and other UK emergency responders) and has been rolled out globally to emergency responders.
SARLoc was originally developed by a Team Member of the Ogwen Valley Mountain Rescue Organisation and records verified hits and uses multiple times a week in the UK alone.
The only time What3Words would make work easier would be if no data connection existed and only voice or text messaging could be used. But in this instance the app would already have to be pre-installed on the user device. Even then, the only benefit would be the ability to phonetically spell words more easily than numbers via a bad line or the ability of W3W to ensure that misspelled words in a text are still pointing to a relevant location.

All in all – as you say W3W are producing a great example of faking Openness and trying to sell people a solution to a problem that by and large does not exist in most developed western nations.