Lol. Calling the Dead the best LIVE band period is to be completely ignorant of all musical talent going on around them, and simultaneously being a fanboy, and a douche. I see how you can argue that in this day and age, studio work is useless because of the high level of production it takes to make a song, and how it's made so easily today. But let's talk about back then - in the early 70's and late 60's - and how what you said is made COMPLTELY IRRELEVANT to the conversation simply by the time frame. The Grateful Dead could not provide a commercial product, nor any groundbreaking material. They never experimented, and the rarely, if ever changed their style or progressed in the entirety of their career. You may enjoy jamming, but saying their live shows were the best denies Hendrix (far superior), The Who (far, far superior), Led Zeppelin, Pink Floyd, Cream etc. from that debate. And truthfully, every one of those artists mentioned above were miles ahead of the Grateful Dead in terms of musical ability and live show playability. Frankly, to put the Dead on a scale, I'd say they were more on par with Jefferson Airplane musically than anyone else. The only difference is that the Dead miraculously managed to cultivate the largest and most dedicated fanboy audience ever seen. This does not make them good.
Now, I'm not trying to say that the Dead don't deserve some of their credit. But they definitely don't deserve all of it, or even most of it. If you've ever heard them sober, you know what I'm talking about.