Key to a good blues band is a good singer who can put the song out there in a believable way without excessive embellishments, a guitar player who can knock out hot solos but slip back to rhythm to let the vocal shine through, and a bass/drums rhythm section that is nothing fancy but holds down the groove like a freight train on a track. And song selection should contain some Chicago-style standards like Key to the Highway, Backdoor man, and Stormy Monday, along with some obscure or Delta-style blues presented in sparse production but danceable. And that may be the real key...blues music, unlike Folk style, needs to be danceable to get the crowd involved.
Harp? Keyboards? Horns? All good, but generally not enough to carry a band weak in the primary areas. I was a rocker who got involved with some blues guys and out of it came my band Terraplane, now in our third decade. We don't meet all the criteria either, but we have one important strength...we all like each other. and that's the last important thing. If one of the people is an asshole, but a great drummer, you may sound good on stage but you'll hate practising, and without practice you won't grow.