Are there big reasons the training can’t be done SETI at home style - you could even pay people for use of their graphics cards and do the training multiple times on different machines to make sure results weren’t being gamed.
Going from that to the dozens to hundreds of milliseconds of latency on the internet, or the hours if you do classical SETI@Home, is a big step. There are people working on it though.
Also gradient updates from all nodes would need to get combined at least every few training steps, and it would take a while to sync all gradient updates across the network.