I've never heard the expression 'siding the pots'! What a curious way of putting it. And I'm not sure what is meant by 'letting the meal settle'. Settle where? Its already in your tummy! The only time I've ever felt the need to sit down after eating has been after Xmas dinner, in which case I'm too full to move!
I suppose if its a dinner party then one wouldn't whip the plates away immediately. That would be rude! But I'm not sure anyone around here lets their dinner 'settle'... they just eat it and then carry on with whatever else they are doing. That's why all the plates, bowls and mugs end up in their rooms or in the cellar (son plays computer games in cellar). If its just me and partner I always clear up straight away, after all, it only takes a few seconds to bung the plates in the dishwasher!