Mine don't leave the table without asking either. That in itself isn't necessarily as good as it sounds when you are asked every 30 seconds if one of them can leave.
School has a lot to answer for. DS1 used to eat with his mouth shut naturally for which I gave myself a smug pat on the back and thought how easy this reinforcement business was. Unfortunately, that ability deserted him sometimes towards the end of the infants. I think eating with others at school is to blame - he didn't learn that at home! I am sure that the school do encourage good manners to the best of their ability but I am on his case throughout the whole meal. They simply don't have the staff to do that for every child.
And I do take him to restaurants and mine are a lot better behaved than some but that doesn't mean that I am able to relax - I still have to micro-manage their behaviour which is wearing.
I don't let mine get away with things either but as I say, I have been doing this for 10 yrs and sometimes, like the OP, I get fed up with it. It leads to bad feeling and fraught mealtimes and the occasional stomping off (mine not the children's - they aren't allowed to stomp without asking obviously.
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I would cut the OP some slack, allow her her whinge and assume that the reason this bothers her so much today is because she does care about table manners and is just having a bad day, not that she doesn't know what to do and is letting her children run feral at the table.