Imagine there was a bijection between model parameters and resulting function. (I'm aware this is not at all true.) In that case it seems like you are enforcing the constraint that the two heads have identical parameters.
AFAIK, I always imagined the idea behind this objective function to be quite similar to contrastive learning, where you have two networks (or equivalently two sets of parameters), and the goal is to maximize agreement for pairs of inputs to each network that have the same ground truth class/label (conversely maximize disagreement for pairs...
It makes sense that negative pairs would help to a large extent, but not all contrastive papers used negative examples, like BYOL (ref). Edit: but now I'm realizing that this might no longer fit the definition of contrastive learning (instead just ordinary self supervised learning), so I apologize about the error/confusion in that case.