This is one of the best answers in the thread.
I'd also add that if they had Marines available nearby,
particularly if they had some combat experience, they almost certainly would have added them to the mix. I don't believe that WW2 had quite the degree of hostility between the services that we see today, or at least not as common. I have my grandfather and father's journals and letters (all scanned thanks to my brother's extensive genealogy work), and there are frequent friendly nods to other branches throughout.
My great-grandfather served in both WW1 and WW2, and his son served in WW2. Notably, my great-grandfather suffered blindness and coughing from a gas attack in WW1, but still signed up for duties stateside in WW2. He would have gladly been on that beach had they let him. His son, my grandfather, came through mostly unscathed physically, but emotionally was never quite the same. He drank heavily after the war, and died a decade before his father did, he died on my birthday so I never got to meet him. He was remembered as a very kind but sad person, with a penchant for practical jokes that were a rare opportunity to see him smile. He also took fierce pride in his 6 children, and when the Vietnam conflict came to pass was really skeptical of the leadership. He saved newspaper clippings of every KIA/MIA from his hometown, and pressed all of his children to study hard, get into college, and avoid the 'tragic waste of precious young people' that he saw that conflict to be. He understood why Hitler and Hirohito had to be halted. He didn't understand why we should get involved in a SE Asian political conflict, not a fan of 'domino theory' I guess.
Anyway, why I think they would have added Marines :
http://www.worldthroughthelens.com/d-day.php
The UK
did in fact throw their Marines into the mix. One might argue in some sense of patriotism or bravado that the USMC is superior, I can't really agree, in point of fact at Normandy they gave just as much as everyone else. In fact, the thing I learned most about all of those letters is just how much we will never personally understand, those of us who were never there. It was a different era entirely, and before long, WW2 will have it's own 'Harry Patch' moment, and there will forever be silence from those voices. Only the dusty books, flickering documentaries, and countless gravesites will testify for those who gave so much.