They knew OMAHA would be tough. But to not attack it would mean opening up a huge gap between UTAH and GOLD. It would leave the airborne force at Carentan isolated without hope of reinforcement. That would allow German reinforcements coming from the south to focus on UTAH, while isolating UTAH from reinforcement from the Commonwealth beaches. It would also mean diverting Mulberry A from OMAHA to UTAH.

There are a couple of very good arguments for not switching troops to another beach.

As RonPossible says, OMAHA was a key beach in the overall plan for Overlord, the invasion of Normandy. Without it there would have been two very isolated beacheads out of mutual [ed] support. The Germans might well have been able to concentrate their forces against one and eliminate it. As subsequent events during the Normandy campaign were to show, the biggest problem the Allies faced was lack of space to maneuver against the entrenched Germans

Furthermore switching the follow on waves to another beach would likely have condemned those already on OMAHA to death or capture. We know the casualties they took getting to and off the beach, now imagine the scene if the Germans could see the troops going down to the waterline and getting ON boats. It would have been catastrophic.

You touched on another reason for not switching: logistics. While many troops crossed the channel in landing ships directly from English ports, large numbers were embarked on large troop transports and then cross-decked to smaller assault craft. Those transports were anchored several miles offshore. To move them would have required several hours of pulling up anchor, marshaling the ships, re-anchoring and coordinating with the forces already at their destination.

Those are all good reasons, but in actual fact the main reason the following waves were not directed to another beach was actually quite simple : command inertia. By the time the commanders offshore had solid information on the state of the landings the crisis was largely over.

Within minutes of the landing the OMAHA plan was essentially shot to pieces. The preliminary bombardment had had no real effect on the defenders and the strong tide and winds had forced most of the landing craft into an uncoordinated bunch on the eastern end of the beach. The gullies which were planned to be the route off the beach were controlled by large bunkers mostly impervious to the weapons the troops had on hand. The result of the chaos and the stiff defense was that the assault appeared to stall at the shingle line. Compounding the problem was that there was little communication between the landed forces and the commanders offshore.

Initial reports from the offshore destroyers. and from an observation group in a PT boat, were that there was no apparent movement off the beaches. This information reached Bradley (1st Army commander) and Gerow (V Corps commander) around 10am, some three and a half hours after the landings started. There was some debate about suspending landings at this time.

However, although the gully exits were blocked, the infantry, working in small groups and in taking advantage of whatever cover they could find infiltrated up the slopes. The first troops on top of the bluffs, and thus behind the defenses, were there by around 8am. Clearing the pillboxes and MG posts from with flank and rear attacks, while tanks and naval gunfire support steadily reduced the bunkers, this effort snowballed and troops began climbing the tracks up the bluffs in sufficient numbers that it very quickly became obvious to the ships just offshore. Another observation group in a DUKW reported around noon that they could see US troops on the skyline. At that point the question of whether to move to another beach became moot.

Also I do want to point out that while casualties were heavy, they were not out of line with predictions.

Primary source: Joe Balkoski, Omaha Beach: D-Day, June 6, 1944, Also Rick Atkinson, The Guns at Last Light.