Lack of trust and failure to rely on Dutch assistance meant that nobody bothered to just pick up the telephone and dial information.
Maybe the whole thing would have worked better if the britts used the resistance a bit better?
The Dutch resistance had been badly penetrated and compromised during the "England Spiel" and by 1944 there were four different resistance groups operating in the Arnhem and Eindhoven area, together with SOE, OSS and combined Allied JEDBURGH teams. Not all of the groups, nor everyone in them could be 100% trusted either by the Dutch or by the Allies. Co-ordination with the Dutch Government in exile command was sketchy because even their Intelligence liasion officer was suspect. Additionally the conventional wisdom at the time in all European operations was not to involve resistence movements too much in fighting as they got in the way. Nevertheless the Arnhem resistance was prepared. The very day before the planned assault MI6 learned that "King Kong" Lindemanns a senior Dutch resistance leader (who actually reported to MI-9) had defected to the Germans. As it happened, although he knew that an airborne assault was coming, he didn't know exactly where or when and thus gave the Germans crap information. Thus British units were given strict instructions not to rely on the Resistance.
What, dear Armchair Generals, what would
you tell your troops in such a situation?
As it was, the troops did indeed, eventually, co-operate with the resistance members in a substantial fashion and some of the most important runners and couriers for the British were Dutch Boy Scouts.
Strange as it may seem to some people, in Holland in 1944, one did not pick up a phone and dial anyone. One picked up a phone and waited for an operator to answer. The telephone system was controlled by the Germans in all occupied countries and at Arnhem was shut down by them as soon as the action started. However, the local Dutch resistence cell actually operated a secret, closed, telephone system that belonged to the Dutch power company and during the fighting Dutch post office workers managed to get the Arnhem system operating in an ad hoc fashion. While Urquart eventually made use of the system from a line especially run to his CP and the resistance CPs, this was 1944--there were not phones in every house and on every corner and besides, as anyone who has been in the military knows, telephones are insecure--even battlefield field phones can be and would be tapped into.
In the end, Frost and 2 Para were doomed because Horrocks XXX Corps had to stop for tea, anyway.
This is just a silly thing to say--and I am being extremely polite.
Answer to original question.
Market Garden was, like all monumental cock-ups, a series of minor cock-ups that individually would not have been crucial. But just so many things went wrong that if any individual cock-up had gone right the end result would not have made much difference. Working radios may have kept headquarters informed of the problems earlier, but it is doubtful that much could have been done.
The problem with Market Garden is that it follows the rule that Victory has a thousand fathers but defeat is a bastard child. No one plays up the equally crass cock ups in battles that ended in victory, like Overlord, The Battle of the Bulge etc. and etc.