Isn't this exactly why browsers implemented "private mode"?
Why don't they inform users about how to properly use private mode, which works with any website, instead of rolling their own solution, which the user has to learn just for that one website?
Private mode assumes you choose in advance. If you are suddenly approached, you can trigger the quick exit without any prior planning and it can be done inconspicuously.
They could be in a situation where that’s not available such as a child’s phone with parental controls or a managed work device that has it locked out.
Because most users aren’t computer savvy and victims in a hurry probably don’t have time for a lesson.
On top of that, informing users requires them to open up the website in the first place… leaving it in… the history.