Hello again, I assume this is the section of keras docs that you are referring to 

Once your model has converged on the new data, you can try to unfreeze all or part of the base model and retrain the whole model end-to-end with a very low learning rate.
This is an optional last step that can potentially give you incremental improvements. It could also potentially lead to quick overfitting – keep that in mind.
It is critical to only do this step after the model with frozen layers has been trained to convergence. If you mix randomly-initialized trainable layers with trainable layers that hold pre-trained features, the randomly-initialized layers will cause very large gradient updates during training, which will destroy your pre-trained features.
It’s also critical to use a very low learning rate at this stage, because you are training a much larger model than in the first round of training, on a dataset that is typically very small. As a result, you are at risk of overfitting very quickly if you apply large weight updates. Here, you only want to readapt the pretrained weights in an incremental way.

That is very interesting.  Chollet is certainly worth attending to!
I note that he was not talking specifically about BERT (or Transformer models).   However, I think I should train my model again, starting with all the BERT layers frozen, and only then unfreeze some of them.
I note that Chollet doesn’t say that training the BERT weights is always Bad, but that we need to use a small learning rate to do so.