It is perfectly possible to teach a dog to walk in a harness, after all you don't see people being towed around the place by Guide Dogs (the pressure they put into their harness is barely anything at all, and they don't pull at all once the harness is off) and most assistance dogs other than guide dogs put zero pressure into their harness at all.
Harnesses do not make dogs pull or teach them to pull... that comment tells me you really don't understand why dogs pull in the first place! (Because they naturally walk faster than us, are rewarded for moving forward by getting to sniff new things/move forward/get somewhere and later in life, because that is how they've always walked).
I start teaching puppies to walk on a loose lead... without harness, collar or lead! Because I am actually teaching them how to walk beside me, keep a good eye on me and ready for the next instruction.
We do that in a secure place with low distraction, high value rewards and build up, and when its a pretty solid skill, then we add in the lead. I prefer this to be clipped to a harness that the dog is conditioned to wear, because IF that dog should stumble, be suddenly distracted, lunge forward because they're startled etc... then they won't hurt themselves.
Doing those things with a collar round the neck can cause injury (particularly soft tissue injury that is hard to dx and treat, one of the leading causes of on-lead reactivity in dogs!).
Why would a chain lead be needed... the only time I have seen it insisted on is where the dog bites the lead (and then I use a cable lead, plastic coated as teeth can get caught in the chain, or broken on it)... dogs can bite the lead to tug it, not wildly uncommon in young dogs...
Or dogs can bite the lead in redirection, aggressive/defensive response to harsh aversive 'corrections' given with the lead/collar - it is a VERY common 'fall-out' with this type of training.