John,
I much approve of your heresy. Your three categories are good - checking, formal training, and informal practice.
When there was some spare sim time, I often asked the trainee if there were some things he would like to practice. Sometimes he only wanted to brush up on a particular handling item, other times I suggested we play some games. He would set off on a normal sector, and I would chuck in some unexpected failures, including some fairly bizarre ones. Then we would all learn something about the startle-factor (not that it was called that then), or about how best to prioritise and how best to use the crew, or even (heaven forbid) throw the checklist out of the window and get on the ground ASAP.
If all this was done in a totally non-threatening manner there was much that we could all learn - including me, as the instructor.