Have tried reins on dd (those godawful pink 'princess' ones as I couldn't find any others - now they're offensive!) and she too did the 'tom-cruise-spinning-on-a-wire-in-mission-impossible' thang, so they have been put away for the time being.
For her it's not so much that she runs off, it's that she won't come in the first place (there are interesting stones, beetles and bits of chewing gum on the pavement to be investigated). Because there's just the one of her, I've had it fairly easy, but I would definitely persevere with the reins if I were to have another child.
An Irish guy I once shared a house with (about 20 years ago now) came home and said in tones of horror 'I saw a child on a dog-lead in town today! Is that what you English do to your children?' - we all fell about laughing, having had reins ourselves as children. As someone's already said, why afford your dog protection that you wouldn't give to your children??
LEM - I haven't done the 'Walk On!' thing , but I have found myself bawling 'STAND!' at dd on the rare occasions when she's about to peg it - surprisingly it works - obv. my horse-scaring voice is far more commanding than my mummy voice....