A proper flute headjoint or footjoint tenon fit should be a metal-on-metal friction fit. This is how they are fit from the factory. My most precise tools in my shop can measure down to .0005 inches. The difference between a joint that is too tight and a joint that is too loose is less than I can measure with these tools. A good tenon fit should not have room for greases or oils. Once these greases are applied the liquids in the grease evaporates, leaving behind a film that becomes sticky. Then they need to apply the grease again.
As a repair person I have from time to time needed to get very badly stuck tenons apart. In nearly every case the owner of the flute has told me that they used cork grease to make the tenon fit. In the few other cases they were hard to remove because of mechanical damage. Never have I had a tenon get stuck so difficult to pull off that it had to come to the repair shop if the tenon was kept clean and wasn’t damaged.
If a joint is having trouble going on or off there are only 2 possible causes of it sticking. Either the tenon is a poor fit or the tenon is dirty, and the dirt is causing the tenons to stick together. If the tenon is a bad fit, then the solution is to fit the tenon. If the tenon is dirty then all you need to do is wipe it off with a clean cotton or microfiber cloth or use some alcohol on that same cloth. I would consider the practice of applying cork grease to metal to be adding things between this very precise friction fit and making it dirty.
Trumpet or trombone slides are designed to have a layer of grease in between the joints, and flutes are not. Brass instrument slides stay together when the instrument is put away in the case, where a flute tenon is removed. On a flute, if greases or oils are applied to these tenons then they are exposed to the air, the case, or the oils of a person’s skin and they begin to pick up dust and dirt. This doesn’t happen with brass instrument slides because the oil or grease is contained in the slides and not exposed to collecting dust. Even so, brass players who take good care of their instruments clean these slides regularly to remove old grease and dirt and re-apply fresh grease.
It is actually fairly rare to have flute tenons get stuck on flutes unless they are dirty or they have been damaged. If you find that tenons are getting stuck a lot it might be because someone is using grease on the flute joints.
When a joint is getting stuck or hard to pull off please first try using alcohol on a lint free cotton or microfiber cloth to clean both the inside of the box or barrel (the female portion of the joint) and the same cloth and alcohol to clean the outside of the tenon (the male part). In most cases this should make it fit well. Then be sure to clean their instruments with a cloth when you put the flute away to prevent the joints from sticking. If cleaning the joint doesn’t help, and the tenon is still a bad fit, then have them take it into a good repair shop to have the tenon re-fit.