Can you trust the model when the people releasing it are using it in this way? Can you trust that they won't be training models to behave in the way that they are prompting the existing models to behave?
For most bikes this ratcheting mechanism is in the back wheel, so when going down a hill the pedals, the chain ring, and the chain are all staying in the same position.
In the demo the chain ring and chain are moving under the motors power, but the pedals are remaining still.
I see these points as reasons why it might not be a good idea, but they don't explain why it is a bad idea.
Other methods for leaving the site still work. Even if the button isn't the best way to leave the site, if it helps in more cases than it hurts then it's a net benefit.
These buttons are essentially panic buttons, and when a person is panicking the big red exit button might end up being the only exit they can find.
This is way outside my area of knowledge, but when under stress do humans actually use things like panic buttons? Or do they fall back on week known patterns of behaviour?
My gut tells me that the big red button might not even get noticed.
But I can imagine that people accessing information about domestic abuse might not necessarily have regular access to internet connected devices, they might not know the best ways to act under stress.
Maybe they won't notice the big red button, but maybe there is some chance that they will notice it, and therefore some chance it will be beneficial to them in that moment.
Governments still have budgets. At the end of the day it's just money in, money out, except private healthcare has someone siphoning money in the middle.