In the end Ike signed off on Market-Garden.
The relationships and egos involved in the Allied Command is a research project of it's own. Monty very much continually pushed the idea of a single ground commander, which he of course saw would be him. It eventually lead to some incredible friction that almost lead to the break up of Allied Command when Ike got to the point he was going to make the Joint Chief's choose between he and Monty. Monty's Chief of Staff got wind of this from Ike's Chief of Staff and was able to put out the fire, which was by finally getting Monty to realize that he was never going to run the whole show with the majority of the fighting being done by US troops and the majority of the supplies coming from the US.
This was post Market Garden during the Battle of the Bulge.
But Ike did have Monty continually pressing for a single thrust instead of Ike's preference for a broad front. And of course you had the egos of Bradley, Simpson, Patton and others to sooth as well. When Monty was given the go ahead on Market Garden, it basically stopped those other guys in their tracks for lack of supplies.
Also understand that the battle of egos was not a British vs American thing, it was individual generals. Air Marshall Tedder who was head of Allied Air Forces in Europe for Ike, was British and he wanted Monty sacked more then once. Beddel-Smith who was Ike's chief of staff spent a lot of his time working with Monty's Chief of Staff to keep Monty in the game. Monty's big fear was that he would be replaced by Alexander, who was in command of British forces in the MTO. It was when he finally realized that was a serious possibility that he finally quit pounding on Ike to appoint a single ground commander.
All that being said, in his quest to lead the single thrust and be the first over the Rhine and into Germany, Monty oversold the plan and ignored much of the intel and the British Airborne guys paid the price.
Ike had the final say however and he signed off on it, so it can't be laid completely on Monty either. My impression has always been that the Brits have been far harder on Monty about Market Garden then the Americans, in particular the British Airborne guys who got hung out to dry.
Cornelius Ryan was one of my favorite authors when I was really getting into the WW2 history stuff back when I was a kid. I wrote a report on "A Bridge Too Far" and Market Garden in high school. Jeez that was a long time ago
The book is far better then the movie, although at the time, the movie did take things up a notch in terms of trying to make it look right.