Actually, I admit, the REAL REASON I do this, is out of laziness, or just because I don't see it as an issue. NOT really to encourage my children's independence. But for my own convenience.
My 2 ds's are so UN-anxious, that they seem to not need me that much. And have always been that way. My friend insists [wink} that this is just their personality and the fact that I have always only ever worked part time, that they have always 'had me around' and thus never needed me.
Well, I liked her suggestion!!

I potter around. Go out gardening, wash the car, pop to the garage, nipp to the shops. When I get back, neither of them have moved an inch and often not even noticed that I've even gone. even though I always tell them that I'm going.
Sometimes I wonder if I died, they might not notice for a week, or until there wasn't any shreddies left, or spaghetti and meatballs wasn't produced and they didn't have anyone to drive them to football practice twice a week, they might finally look up and go :
"where's mum"?
I think I saw a week last Tuesday .......