Our language processors have much lower latency and higher throughput than graphics processors so we have a massive advantage when it comes to inference. For language models particularly, time to first token is hugely important (and will probably become even more important as people start combining models to do novel things). Additionally, you probably care mostly about batch size 1. For training, latency is not the key issue. You generally want raw compute with a larger batch size. Backpropagation is just a numerical computation so you can certainly implement it on language processors, but the stark advantage we have over graphics processors in inference wouldn't carry over to training.
Does that answer your question?