Hold on, you don't even need to freeze the branches completely: each node could train 1 branch on the path to its leaf node and communicate a change in the branch node to a central server, so you can distribute training without having to pre-freeze the branches. Still would need some pre-training though, and the splits would change slowly, and the attention mechanism could complicate things.
Currently distributed neural network training SETI@HOME style looks like a complete pipe dream that nobody is taking seriously. But a smart branching mechanism like this could suddenly make it possible. Folding@home reached 1.5 exaflops, which made it the world's largest supercomputer. Imagine the models we could train that way, they would far surpass whatever OpenAI or Google could train and would be public.