But the problem is, sir, that doesn’t answer the question, about whether or not landings on Normandy could have succeeded if Omaha Beach weren’t even in the picture, resources for there sent to the other four fronts instead, to ultimately “pinch” Omaha from below.
Bottom line. It worked, though at great expense of lives it worked.
If the question is 'should the planners have left Omaha out' then the answer not relevant. What they planned for and what happened are two entirely different things. They missed landing areas, they didn't know they were facing experienced troops, they underestimated the length of open beach they would have to cross, and they especially did count on all the DD tanks sinking before making the beach.
Very little of Operation Over-Lord went as planned, however, that is exactly why it was such a success (i.e. paratroopers scattered all over the Cotentin Peninsula confused the Germans and prevented them from mounting defenses).