To get to the basic thrust of the OP I agree with you that the "That is MY mug!" syndrome is very unpleasant but I can also see in the workplace where one is unsure of the washing up skills of ones workmates then to have a "My Mug" is prolly a good thing.
At home, and here I am being serious, we try to teach our children to handle anything that they may encounter in their future lives.
One way to achieve this is to introduce them to cups, saucers, cake plates etc. Teach them that smoked salmon sandwiches should come in brown bread with a squeeze of lemon and a little black pepper, small cakes and pastries are served using tongs from a two or three tier cake stand. There is a difference between napkins and serviettes. Small talk is acceptable and should be deployed at the table. In fact our usual Sunday routine is that we all sit in the dining room together for breakfast, lunch and dinner. The full set of appropriate tablewear is put out and we insist that everone sits down at and leaves the table together.
I don't see this as being posh but as part of their education, just as both boys have been taught to tie a bow-tie (I hate those elastic things)
Of course on every other day of the week it is a bloody free-for-all with food eaten on the run whenever we can fit it into the schedule of activities, tea and coffee are consumed out of whichever mug/cup/jam-jar comes first to hand .... much like most other people then but, as I constantly remind the children, you never know where you might be invited so it is as well to know how to behave.