I believe the reason for a lack of close air support despite almost total Allied air superiority was due to a problem with the radios. I can't remember the exact radio frequency problem, but there due to the ground forces having a higher frequency signal than what the RAF fighter-bombers was using. If I can remember correctly, the 1st Airborne Division, the only unit that could contact the RAF either couldn't calibrate their radios correctly or lost them in the ensuing chaos.
Coupled with the rather poor weather, it meant that fighter-bombers couldn't engage any targets due to a risk of friendly fire.
There were several problems with air support from 2nd Tactical Air Force at Arnhem. Poor weather disrupted flying operations for both 2nd TAF and the transport aircraft dropping troops and supplies, and 2nd TAF were forbidden from flying missions while transport aircraft were operating. Co-ordination between the various headquarters was poor, in part due to the hurried preparations, so there were instances where 2nd TAF were unaware of changes in plan due to the weather over English airfields or the drop zones.
Around Arnhem, 1st British Airborne Division had serious communication issues (detailed in the paper [Assessing the Reasons for Failure: 1st British Airborne Division Signal Communications during Operation ‘Market Garden’] (http://www.tandfonline.com/doi/abs/10.1080/1470243042000344777)), both between formations within the division and to other units. Two US Air Support Signals Team from 306th Fighter Control Squadron dropped with 1st Airborne, equipped with Very High Frequency jeep-mounted radios to call in air support, but according to Arnhem: A Tragedy of Errors these had only been issued a few hours before departure and the signallers were unfamiliar with them, they were supplied with the wrong crystals so were operating on the wrong frequency, and the jeeps were destroyed. Requests for air support did reach 2nd TAF via other routes, but with a fluid battlefield, messages passing through multiple other units and no immediate controller on the ground many were rejected, either due to the aforementioned weather/co-ordination issues, or because targets were insufficiently identifiable.
Although Old, Cornelius Ryan's "a bridge too far" is an excellent read for the entire operation, and although to my recollection doesn't specifically answer the question, it does provide the bits and pieces (the osprey books on the operation, by Steven Zaloga, are also quite good for a good overview):
there were radio failures and communication problems from the get go, especially for the British 1st airborne division, their radios were hampered by short range, issues in the wooded AND city areas they were covering, on top of this, the tactical radio nets allowing for this type of coordination were not really well thought out on the airborne side (on the other hand, xxx corps had a number of embedded Forward air controllers, and brought down numerous typhoon strikes throughout their advance)
the terrain and built up nature of Arnhem and its environs in particular did not really allow for clear, markable targets for fighter/bombers, and the inaccuracy of medium/low altitude bomb runs would have made that form of air support impractical, allied command was wary of "close" bomber support ever since an incident right before operation cobra were a number of Americans were killed and wounded by friendly bomber fire.
weather also played a large part through the operation, from the 17th to the 25th, weather over both England and the Netherlands was temperamental, it took all the way until the 21st for the parachute elements of the polish brigade to drop, weather at the time was a major factor in CAS missions, and precluded fighter bombers from flying (this would be repeated later on in the Bulge, where allied air superiority was suppressed due to weather, allowing the Germans a chance to attack)