Datasaur are great. I hope Ivan would think it's fair that I'd describe their current product as as a modern, cloud-hosted Brat (https://brat.nlplab.org/ – this remains very popular!) with the features to make that work with teams. As you point out we're focusing on the tight integration of annotation and training enabling you to move faster and iterate on NLP ideas... essentially trying for move a waterfall ML lifecycle to a an agile one.
Fine tuning on BERT is the way to go. It's what we do, and that already reduces the data annotation requirements by an order of magnitude. Doing that offline in a notebook is still wanted by some (you can use our tool just as the annotation platform, and download the data and you'll still get the efficiency benefit through active learning) but integrating or deploying that model is still a time-suck. Having the model deployed in the cloud immediately has a load of supplementary benefits (easy to update, can always use the latest models etc) too, we hope.
(edit: typos)