The flotation screens that led to the Sherman DD were being tested, fitted to tanks, in June 1941, before the first LVTs were made. After the initial tests, most of the early amphibious tanks using such flotations screens were based on the Valentine. The flotation screens were a British development, hence the use of the Valentine. As the Normandy landings approached, it was decided to switch to the Sherman, since it was a much better tank than the Valentine.

The first LVT that was really useful for fire support was the LVT(A)-4, with a 75mm howitzer, and light armour. This was ready at about the time of the Normandy landings, first going into action in the Battle of Saipan. Before this, there was no LVT that offered serious competition to the Sherman DD for fire support during landings. The Sherman was much better armoured, and also better armed - its gun was more useful against enemy armour, and unlike the early LVT(A)-4, it had machine guns. Given that Sherman DDs were knocked out by German anti-tank guns at Normandy, despite their quite respectable frontal armour, LVTs would have suffered far more from German fire.

Also, at the time, there were few LVT(A)-4s available, and since they were able to cross coral reefs that would stop boats, they were very useful in the Pacific. No such inconvenient reefs were present at Normandy, and conventional landing craft could land infantry faster, with Sherman DDs providing better-armoured fire support.

The LVT(A)-4 saw use in Europe later, such as during Montgomery's crossing of the Rhine and the Battle of the Scheldt:

• https://commons.wikimedia.org/wiki/File:The_British_Army_in_North-west_Europe_1944-45_B11628.jpg

• https://commons.wikimedia.org/wiki/File:Acrossthescheldt.jpg

and in Italy

• Crossing the Po: https://i.pinimg.com/564x/e6/21/ea/e621eac6d147c152712f4800a3a097b4.jpg

LVTs were used in the Normandy landings, but these were unarmoured, and without guns useful for fire support. They were used for the role that the LVT had been originally developed: as a transport vehicle, ferrying supplies and equipment from ship to shore at Utah Beach and Omaha Beach (the DUKW saw extensive use, too, carrying about 1/5 of the cargo to shore at Normandy in the 1st month after the landings). They had also been used in Operation Torch, similarly for transport.

Lifting a sunken LVT from the Maas after the war:

• https://www.strijdbewijs.nl/landing/lvt0010.jpg

(photo from https://www.strijdbewijs.nl/landing/landeng3.htm which has plenty of photos of amphibious vehicles used in Europe after D-Day). I think this is the same LVT that ended up in the Buffalo Memorial: https://worldwar2revisited.com/2016/01/17/buffalo-lvt-memorial/ ("Buffalo" being the British/Canadian name for the LVT).

For more details on the LVT and their use in the Pacific, see the reply by u/the_howling_cow to a very similar question in https://www.reddit.com/r/AskHistorians/comments/4sz7lr/why_wasnt_lvts_used_at_dday_beach_landings/