The landings, and here I speak of the American landings as I never claim to know much about the Commonwealth beaches, were actually pretty well planned and choreographed with specific fire and maneuver tactics. Yeah, you think we took the beaches by having a mass of materiel?
The Assault Training Center was set up to figure out the best way to take the beaches. That is what they did, and they did a pretty good job of it. They made the conscious decision to not put all their eggs in one basket, and divided the firepower up throughout the boat teams. First you land the DD tanks (before the infantry so they don’t get driven over) and hopefully the Germans go "Vas ist das?" and flip out. Just behind them come the assault teams, and together they would try to knock out a number of the defending positions using a combination of 75mm gun, bazooka, flamethrower, explosive charges, and plain old hand grenades. In doing so these groups (and tanks) posed the largest threat to the Germans, which hopefully kept them from firing at the gap assault teams that followed.
Then you take a break and let the gap teams do their thing, then you bring in more assault boat teams to reinforce the first wave. All this time the assault teams are using fire and movement to get to beach defenses, pin down the men firing from the embrasures, and allow others to get into a position where they can take the bunker or MG nest out. This was planned and practiced many times, and the variety of weapons allowed them work in different ways, and be able to continue to function if part of the team was knocked out. Diversification at its best.
Of course if you land in the wrong place you have to toss away all your planning, but by having the mixed teams they could take on anything they ran into. Did it always go as planned? Of course not. There were things that went wrong, and things that went right. Mainly the use of individual initiative that we Americans are supposedly known for.
But the US army DID NOT push man after man onto the beaches and into the jaws of death as a human wave.