I think this would be hard to organize in a competition. The problem that seems most obvious is that teams may interfere with each other since oral communication is necessary. It may be hard to hear when many attempts are happening concurrently and hearing others' solutions would bring cheating potential (it might even just inadvertently affect the blindfolded person's state of mind - very hard to unhear something). Personally, I'm not a big fan of introducing new 3x3 variants. Team BLD seems to be quite optimized already, and the solving style is almost identical to normal 3x3 speedsolving from what I understand, as long as both teammates have names for a sufficient number of F2L and last layer cases.
Additionally, the number of people that would be able to compete at a high level would be severely limited through circumstances not their own. You would generally need a partner at or higher than your level in speedsolving ability and knowledge to reach your "full potential," and naturally it would be even harder to have record-breaking potential.
Maybe conventions would develop so that people "in the know" could partner with anyone else with knowledge of the same convention, but to me that sounds quite uninteresting on its face. This would further exacerbate the problem of people hearing others' solutions (imagine you're sitting in a waiting area and happen to (or intentionally) hear someone's solution). Additionally, it would likely still be advantageous to practice and compete with fixed partner or small group of people, for example it would be near impossible to innovate without a dedicate partner. I think we should stick with individual events only. Knowing/competing with other fast speedcubers should not be a prerequisite to becoming fast yourself and team events would essentially bar people from certain areas of the world where there are not many fast people from being competitive on the world stage. (I understand not everyone competes to become world-class, but if it's just for fun I don't see a problem with simply holding it as an unofficial event.)
