The purpose of the airborne soldiers was to capture key strategic objectives like bridges, artillery batteries, causeways and crossroads. They weren't there to take the beaches from behind.
As to why they weren't bombed or shelled, they were, and brutally, and were reasonably effective. However, if it was so simple the First World War wouldn't have lasted four years.
D-Day could have been far worse than it was. It could have been a catastrophe but the planning paid off and it was very successful.
People get a false impression because of Omaha but that was a fuck up, most specifically they didn't have Hobart's funnies and they launched the DD swimming tanks at 5,000 yards in unsuitable conditions and young Americans paid the price. However, that was completely unrepresentative. The landings were a big success and the only major setback was caused by arrogant American commanders.