I personally have no problem with CC being "in the loop" when it comes to a few of the basics from the pointy end. Before I was in aviation I was a manager in a transport company. I brought in a programme of all staff spending a few days shadowing staff in other areas of the operation, office staff with drivers, loaders etc. If nothing else, you get an idea of what each other do, and are more aware of the difficulties each other face at different stages of a flight/delivery route (delete as required) - armed with this information, it is easier to work together as a cohesive team. Shutting engines down, I would rather keep that role form myself/my FO though, there are too many inter-related systems connected to them.
As for simulated non-normal/emergency operations in flight - NEVER!!!
RIX