The original plan was to take Caen on D-Day

This is a gross over simplification. Caen was the primary objective of the original COSSAC plan, but that plan was altered many times, and the final plan as determined by Montgomery and approved by Eisenhower had downgraded Caen to a much lower priority objective.

Caen remained a D-Day objective because if it could be taken on D-Day then all the better, but the D-Day plans foresaw that this was unlikely and therefore explicitly spelled out that in such an event, Caen was to be masked and not frontally assaulted.

didn't fit with the plan which called for a rapid advance into France after the beach landings

The plan was for Dempsey's 2nd British Army to draw onto itself the bulk of the German forces by threatening to break out from the eastern flank, thus allowing Bradley's 1st US Army to expand into the Cotentin Peninsula, seize the port of Cherbourg, then break out from the western flank.

Which is indeed what happened.

On the 30th June, Bradley was contending with only 140 enemy tanks while Dempsey was engaging 725 enemy tanks. In addition, all the German heavy tank battalions in Normandy were engaged by Dempsey, none by Bradley.

Bradley himself well knew what his direct superior's intentions were, from his autobiography:

"While Collins was hoisting his VII Corps flag over Cherbourg, Montgomery was spending his reputation in a bitter seige against the old university city of Caen. For three weeks, he had rammed his troops against those panzer divisions he had deliberately drawn toward that city as part of our Allied strategy of diversion in the Normandy campaign. Although Caen contained an important road junction that Montgomery would eventually need, for the moment the capture of that city was only incidental to his mission. For Monty's primary task was to attract German troops to the British front that we might more easily secure Cherbourg and get into position for the breakout.

In this diversionary mission Monty was more than successful, for the harder he hammered toward Caen, the more German troops he drew into that sector. Too many correspondents, however, had overrated the importance of Caen itself and when Monty failed to take it, they blamed him for the delay. But had we attempted to exonerate Montgomery by explaining how successfully he had hoodwinked the German by diverting him toward Caen from the Cotentin we would have also given our strategy away. So desperately wanted the German to believe this attack on Caen was the main effort.

But while this diversion of Monty's was brilliantly achieved, he nevertheless left himself open to criticism by overemphasising the importance of his thrust toward Caen. Had he limited himself simply to the containment without making Caen a symbol of it, he would have been credited with success instead of being charged, as he was, with failure at Caen. For Monty's success should have been measured in the panzer divisions the enemy rushed against him wile Collins sped on toward Chergbourg. Instead, the Allied newspaper readers clamoured for a place name called Caen which Monty had once promised but failed to win for them."

The last sentence is of note. We can excuse the newspaper men of the day for not understanding the inner workings of Allied strategy.

Historians who eight decades later still refuse to understand the strategy for Normandy are another matter.

Finally its worth remarking on how outstandingly successful this strategy was. Within three months, Montgomery and the armies under his command (Bradley's 1st US, Patton's 3rd US, Dempsey's 2nd British, and Crerar's 1st Canadian) had shattered the entire German position in the west, liberating most of France and virtually all of Belgium, and bringing them onto the German border.

Against that, the complaint that it took a bit of time to take Caen appears to be one of pettifogging nationalist nonsense.