Withdrawing to the Rhine in mid 1944 would have placed the westernmost German industrial cities eithr in allied hands, or within very short range. The Rhine and seveal tributarys were (still are) a critical transport conduit. The maps I have here show several important looking railroad trunk lines close to the Rhine (some on the west side).

With the Allied armys non the Rhine, their airfields will very soon be just minutes away from the Ruhr indutrial cities. With the USAAF & RAF medium bombers in close range the weight of bombing is nearly doubled. Historically the Allied medium bombers in January-Febuary 1945 made an attack on the German transportation system similar to that made on France & Belgium in the Spring of 1944. The results were equal if not better. So retreating to the Rhine early alows such a 'transport attack' to be made that much sooner.

A few days of planning is suffcient to get around traffic problems for some 'bridge columns' . The US First Army managed to rush the necessary equipment for two pontoon bridges & a ferry company to Remagen in less than 30 hours. Additional bridge equipment was brought to the Rhine in just another 48 hours by the First Army. That was without any preplanning, but started with tossing away the existing plan for bringing the bridge & ferry equipment forward to other locations and starting with a blank paper shortly after the Ludendorf bridge was captured.

I cant speak for the British.. The US 1st & 3rd Armys got around the channelization problem by crossing at as many points as possible.

Basiclly I see retreating to the Rhine as placing German industry at increased risk. Making the air bombardment equation simpler for the Allies. Intially the Germans get a small break as the Allies still must rebuild their newly accquired tranportation routes & establish forward supply depots. Historically that took a bit less than three months.