I'm trying to envision the attacks and countermeasures for this approach. I suppose what I would do to fake this is write a program that takes text and the desired output histogram of edit timings and randomly introduces jitter into the typing. Then, I'd imagine you'd develop more sophisticated statistical tests, and so on. My intuition is that eventually there would be no statistical test that reliably discriminates real human typing.
On the other hand "Failed a Turing test" would be a good bumper sticker.
It was not, however, and I found the experience both disturbing and thought-provoking. I actually care about what I write. Being taken for a machine was not something I could have predicted would happen in my lifetime.
I don't think we can really win this fight with technology, but we can take a stand and have fun in the process. So I set up a team of agents to make https://possiblymadebyahuman.com in a (probably futile) attempt to let people claim their humanity.