I have noticed from time to time people who train obedience with their dogs who are more advanced/professional, say that they do NOT train heelwork ON LEAD.  (Someone recently on this Site made that comment too).  Could I ask why that is?  Sorry to sound dense, but i have problems ON lead training let alone OFF lead!!!  (and if you don't ask you don't learn).

Is there an advantage or reason for not training heelwork on lead? 

normal lead work is different to competition heelwork.
although i do use the lead in training with my currant dog,with my bitch i did very little on the lead as she was very independant & alot better"hands off".

also as you cant use the lead in the ring (beyond a basic level) some dogs are better not learning to rely on it too much

It is something I was taught by a retired police dog handler many years ago when I started to train someone elses dog that had been to a"dog breaker"who had abused her using the choker as a punishment. She could not be trained with any sort of collar on at all, he had had a gifted dog that could not be trained on a collar too & had developed an off lead training method. You need somewhere were there is little distraction & lots of patience & treats & interactive toys(like tuggies)

I start with puppies from day one & do a couple of minutes a day & as puppies are at an age when they will follow naturally you are using a natual training tool.

It does mean that when you do put a lead on the dog will follow & walk tio heel because they want to not because they are compelled to by restrint & IMHO I acheive a more natural working position