Though the lack of a screen and camera would seem to neuter the glasses, dropping them would dramatically improve its battery life. And in any case, the idea is not to have Google Glass-like vision, but to give users a direct line to Alexa on a smartphone without having to open an app, as is currently the case. That would make them much more useful in a vehicle or on the street, especially if they can be incorporated into comfortable, daily-worn eyeglasses.
On top of that, the lack of a screen would simplify the development process considerably, reducing the time to market and increasing its chances of success. While Amazon's popular Alexa Echo devices are arguably the king of digital assistants, it's easy to forget the retailer had a string of failures before that, especially the Fire Phone. If "Alexa Glasses" or whatever is a hit, then it might embolden Amazon to offer a camera- or screen-equipped model.
Amazon's top-secret (whoops) Lab126 group is also reportedly working on home-security products, particularly a connected security camera not unlike models from Nest and others. It could be controlled by Alexa-enabled Echo products, and show the video feed on Amazon's Echo Show screen (above). It could also signal you when an Amazon product has been delivered, completing some kind of weird retail loop.
Adding merit to the FT report (which hasn't been confirmed by Amazon), Google Glass founder Babak Parviz, hired away by Amazon in 2014, has been reportedly heavily involved with the Alexa glasses project. Given his area of expertise, it seemed inevitable that Amazon would do something spectacle-related. The eyeglasses and security products are supposedly coming by the end of the year, presumably in time for Christmas.
Update: Amazon tells Engadget that it has "no information or comment" about the Alexa-powered glasses.