That's effectively what Utah Beach was about, land right at the base of the Cotentin Peninsula, and then race west and hopefully capture Cherbourg before the Germans had time to reinforce it.
Which worked, more or less. The resistance in the Cotentin was greater than anticipated, but the defense was not reinforced to any useful degree.
A couple years ago I stumbled across a description of a British plan, dating back to the summer of 1942, for landing a army of 11 divisions in the Cotentin. The initial landing site was the Madaline beach are that was designated Utah Beach in the Neptune plan.
There are also claims Monty briefly looked at the possibility of a landing on the west side of the Cotentin, with the object of breaking the stalemate in Normandy. The exact date was not provided, but it appears to have been in late June.