Another option would be to set the text caret inside the text box, but allow people to write anywhere, while the focus is on a text field. This is probably something where you'd have to do a ton of different prototypes, and see which one feels best.
Agreed that there are plenty of ideas that warrant prototyping, but I think there is special value in not having a text cursor to manage at all, similar to how touchscreens obviated mouse cursors for certain tasks.
