I think Thiers is worth reading, since it seems to make more sense and is more complete than other tales I've read here.
page 536, "Colonel Moutfort, of the engineers, who replaced General Rogniat, who had left for Weissenfels, had been much struck with the difficulty of making the whole army defile by a single bridge of great length, that from Leipsic to Lindenau. He had, therefore, proposed to Berthier to throw other secondary bridges above or below, which should serve for the passage of the infantry, so as to reserve the principal road for the artillery, cavalry, and baggage. Whether it was that Berthier, still sensible of the trouble incurred by speaking to Napoleon of retreat, did not venture to revert to the subject, or (which is more probable) from his inveterate habit of trusting all to his foresight, he repulsed the colonel, saying that it was necessary to obey the orders of the emperor, but not to pretend to anticipate them. Perhaps, also, Napoleon had considered this matter, and had been unwilling to order anything which might too soon betray his retreat. However this be, they were voluntarily reduced to the single bridge of Lindenau, which in certain cases might be attended with extreme danger.* "
* is a footnote on page 536 that directly addresses this exact issue about N., B. the bridges. It reads, in part, " No circumstance In this campaign has occasioned more controversy than the existence of only one bridge to effect the retreat from leipsic. Writers, whose ordinary theme Is, that in his whole life Napoleon was never guilty of an error or an omission, profess that he ordered Berthier to throw several bridges either ahove or below that of Lindenau, and that Berthier failed to execute this important order,. . ."
See History of the Consulate and the Empire of France Under Napoleon, Volume 4 by Adolphe Thiers, 1879
General Rogniat was head of the engineers and had been sent to put up bridges over the Saale. Moutfort, being replacement and only a Colonel, it's easy to see Berthier brushing him off. Assuming that Thiers description of events are correct, Colonel Moutfort certainly thought temporary bridges were needed and possible to build; bridges were contemplated either above or below the current bridge for travel by foot only.
The only remaining question would be why there was no order? In either situation, Berthier is the guy who failed. If N. issued the order and B. failed to execute it then that is a pretty remarkable thing to have happened and presumably would have been commented on by N.; who seemed eager to point blame at others. So, unless there was something about this in N.'s memoirs, it's hard to put much faith in this being the failure of B. at Leipzig due to not following orders,
The story of the Colonel, on the other hand, makes a lot of sense. Word of an expected retreat was circulating and he is the guy who would be responsible for any temporary bridge building it only makes sense that he would have evaluated the situation, and with the need for more bridges being pretty obvious, that he would have gone to headquarters inquiring about his fulfilling this need. Berthier, who had a bad reputation for making decisions on his own,
looks to have made another bad decision when under pressure.
Easy to see why Thiers comes under criticism since he makes every effort to provide a balanced view from the French perspective and is willing to criticize N. He also makes no effort to hide his contempt for the Neo-Bonaparte writers and their attempts to rewrite history in N.'s favor; something that seems to be very much as active today 136 years later.
Thiers' footnote on page 531 is worthwhile reading and applies just as much today as it did then.
So, Digby, it certainly looks like there has been a long push by the fans of N. to place the blame for this on B. for not following N.'s orders. The more likely story appears to be that B. brushed off the responsible engineering Colonel. In either case, B. takes a hit. In one, N. is blameless in the other he carries the blame for not issuing the important order. No matter what, the retreat seems to have been very poorly organized and that would be N.'s fault.