The last hidden layer outputs a vector which is then used to predict the probabilities of every token in the vocabulary, by a single layer (and, in practice now in llama models, this layer is the transpose of the embedding layer).

That vector has a lot of information in it, it's not a debatable thing.

As noted above in parens, look at the llama 3.x models. The space is already shared in some sense. It's called "tied embedding".