That's correct. You can think of the Normandy invasions as succeeding in slow-motion. Planners were hoping for results on D-Day, but it took 10x to 100x longer than expected to achieve each objective.
Caen (port area up to 9 miles from the beach) was a D-Day objective, but depending on the area took 1 month to 3 months to capture. The Allies were slow, and the Germans knew it was a strategic location. Regardless, it just meant that the German army was destroyed around Caen, instead of elsewhere.
https://en.wikipedia.org/wiki/Battle_for_Caen
Of the 5 landing sites, Omaha Beach was the bloodiest, with Americans wading ashore into machine gun fire, killing around 2,000 Americans.
(In Italy and Holland, Americans were also mowed down as the Germans retreated.)
The most famous disastrous amphibian landings were Galipoli in WW1, where the British failed to break out of their beach heads, and also lost numerous ships to mines and shore batteries. This tarnished Winston Churchill's reputation for decades. The victory by Turkey led to its rise as a modern state.
And the US struggled with 3 landings (Anzio, etc.) in Italy in WW2 due to General Clark and his staff trying to consolidate beach heads before breaking out, allowing Germans to occupy high ground, after the landings!
https://en.wikipedia.org/wiki/Battle_of_Anzio#Breakout
Literally, the Americans would loiter on the sand instead of sending a dozen troops to secure roads and hills before the Germans arrived with artillery.
The US had phenomenal leaders in the Pacific War, but Italy was a total failure in multiple dimensions. Historians today just laugh at our role in Italy - it was that bad.
(The British had the weird problem that upon reaching the beach, soldiers would sit down and start making tea, even under fire.)