When do you prefer to code an application without framework?

There is always a loophole for security leak while working in corePHP. You should go for corePHP for the application for which you don't care about security leaks etc and small in volume.

When its an internal quick/small application, for public facing sites always use a framework

Almost notepad is the best way hands on practice to use an application without any framework

when coding small or personal websites which have no users input or db queries.

when building something that you can finish in two days as maximum without the need to look at security and risks .