Brooks delta do have their issues that goes without saying. One of these is that they hemorrhage airspeed in a turn or a pull out from a dive. We wont even get into the loss of power on takeoff, and the list goes on. But they can fly slower at any given AOA than any conventional plane form. Now as far as their efficiency being in a narrow range, I not so sure that is true, where this plane form is found in both GA aircraft and high speed craft like the Valkyrie, Concord and Shuttle.
I can envision a 8-10 ft wingspan delta that has a wing loading in the 4-5 oz range, and carry the type of payload that he need to get airborne and be functional for a long duration flight. Where his requirements for speed isn't that high he wouldn't need a lot of power to get it or keep to airborne and it would be able to shrug off over speed conditions where a high aspect sailplane pieces would be fluttering to the ground.