I make sites for non-profits regularly and have been asked to add exit/escape buttons a few times. There more time Ive spent thinking about the problem and researching solutions the more I think they are a bad idea.

1. Lots - if not most - traffic is from mobile these days. Most people already know the fastest way to exit a page on mobile - the home button/action. Adding anything else is just adding confusion. 2. Unless you are going to great lengths - ie pre loading a page and maybe dropping parts of the dom and dealing with evidence in the history - are you actually doing anything much to help the user exit your site? How motivated/skilled a person are you defending against? 3. If your exit button is just a glorified link or redirect what is the point? It will still be in the history and if they have slow internet they could end up just staring at your site while the redirect loads. 4. For some organisations having such buttons is more about "showing" they have it than how useful it actually is to the user. 5. I have tried to push for a page/link to basic internet safety information. Educating visitors would be much better than trying to engineer their personal security day. 6. I've struggled to find good academic/research work on such features. Seems like it would be a good area for a UX researcher but I've not found much actual work.