Might I play devil's advocate for a minute here?
I have a friend - a dressage rider, and a dedicated one at that - who a few months ago was told by her coach she was ready to start using a double bridle with her horse. This horse has had HUGE problems with working forward into the contact and has a tendency to suck back behind the bit into false collection. Bearing in mind my friend has tried several different bits on this horse all with the same reaction. In a snaffle he likes to suck back and she has struggled for YEARS to get him to the level he is currently at [Medium in Australia, not sure what that translates to in other countries?]... this horse is ALSO not built for dressage, with his long back and interesting neck set.
My friend was very concerned that with the double she would immediately have a horse that sucks back off the contact again. More metal, more bit, more leverage and more to suck back away from.
All of a sudden she is no longer struggling to get him to seek the contact, he actually stretches forward and down for it and is working very well. He has numerous wins and places from Prelim right the way through to Medium over the years and the scores they achieve as a partnership are improving all the time. The horse is much improved upon his muscling from this time last year, and two years ago, and three... I think it's 4 and a half years now that she's had him? He looks simply superb [though he still has an icky neck due to the fact that he is a bad cribber, it is much improved on what it was when she got him!!].
The OTHER factor in play is rider confidence - does the bit cover up the problem, or does it encourage the rider to feel more able to push the horse forward and thus have it going more correctly? You really can't know until down the track when either the horse is getting progressively harder and its muscling is getting more and more incorrect... or it is improving.
My lad is currently in a pelham with double reins and with my confidence much increased due to knowing 100000% that I can keep him well in hand, I am pushing him from behind much better, he is actually flexing in his turns and he will reach for the contact regardless of the length of rein I give him. If I back off the forward and keep the same contact [same bit] he pokes his nose, falls onto the forehand, and stops flexing to the left. Same issues we have in a snaffle - which we have BECAUSE I don't push him forward enough, because I lack far too much confidence, and don't trust him, after all the times he has taken off with me, bucked, or otherwise ditched me. Which, of course, all stem from ME and how crap a rider I was when I first got him.
A CLEAN SLATE FOR THE FUTURE