I just finished watching the first 30 minutes of Saving Private Ryan again. As the ramps for the troop carriers dropped, the soldiers were hammered by machine gun fire. It seems like it would have been so basic and easy to have a metal shield available that the soldiers could carry and hide behind as they exited the boat. Why wasn't this done?
In short steel gets heavy.
While the thickness of steel required to stop a German HMG bullet from penetrating and be large enough to provide real protection is pushing 100 pounds or more. Meaning you get slow men trying to walk up a mostly coverless portion of sandy beach, or worse yet, trying to wade through water, presuming they haven't drowned from the weight or let it go.
That means the goal of getting a sufficient mass of men under cover on the beach takes longer, which means the task of actually assaulting the remaining gun positions sweeping the beach takes longer.
Meanwhile it is of dubious need in the first place. While in certain sectors the beach was narrow enough that MG positions above the dunes could sweep landing craft like in the movie, in others it was beyond their effective range. Meaning the greater immediate danger belonged to artillery like 88mm guns or mortars. Lugging around a heavy shield would just make you a slower target in the dangerzone longer.
And as a final aside it was planned to give the infantry some nice big metal barriers the size of a large truck, and they could fight back, IE tanks. But the spectacular failure of many of the DD tanks put paid to that plan. While other vehicles like the LVT that would provide additional cover to landing infantry were being hoarded by the Marines and Navy for the Pacific and the litany of landings there, while previous landings such as Sicily, and in Italy had been near run at times but been carried off by the Allies in Europe with success in the end.
If you're just getting interested in this stuff, Here's a great essay on how it really went down.
Saving Private Ryan does a chillingly wonderful job of depicting the landing, but it simplifies things a bit.
The movie makes it seem as though Captain Miller's squad was in the first wave at Omaha and made it up to the seawall, and the heights above, in short order. In truth, the first wave was basically wiped out. Most of those who survived did so by hiding or floating in the surf with only their noses exposed so they could breathe.
Omar Bradley was very close to not ordering any more troops into the slaughter. I guess it's a good thing he decided to keep up with it.
Assault from the sea is the toughest attack problem in the book. There's just no easy way to do it against a fortified position. The technique that seemed to work best was to get a whole lot of troops on the beach as fast as possible, knowing that a percentage of them wouldn't make it. There was a cold-blooded arithmetic to planning the assault. Rather than having a smaller number of men carry heavy, buttletproof shields, the plan that worked best was to have a large number of men, lightly armored, get in the Higgins boats, sail up as close as they could, and run for the seawall. History has shown that this method does work. It is bloody and terrible, but it works.
As others have posted, armor was supposed to have been there, but the tanks foundered badly in the channel. All that was left was the men in the Higgins boats. Those who could got ashore and started improvising.
Speaking of improvising, one of my favorite D-Day stories, which could be a Spielberg movie in itself, is that of the destroyer U.S.S. Corey. The Naval armada was supposed to stay safe behind their smokescreen and shell the enemy fortifications from a mile away.
After watching the armor sink in the surf and the helpless first wave get slaughtered, Lieutenant Commander George Dewey Hoffman, the Captain of the Corey, told his sailors, "We are expendable on this mission," and charged towards the beach. There were mines and sunken obstacles, but Hoffman ignored them. He got as close as he could and engaged the German gun emplacements at short range with his five-inch guns.
It was the improvised efforts of men like Hoffman which won the Battle at Omaha Beach. It had been planned as well as an assault like that could be planned, but, as the old saying goes, no battle plan survives first contact with the enemy. Once the soldiers have engaged, you have to trust them to find a way to win it.
There is actually an older thread on this that had a few good points. It probably isn't as comprehensive an answer as it could be.
Becauase any shield strong enough to protect the holder from machine gun fire would be wayyyyy to heavy for a soldier to carry. Theres a reasons shields havent been used since gunpowder was adopted.