Not completely true. I’ve been shore diving from Ft. Wetherill in Jamestown RI many times. There’s a decent amount to see. But diving in the middle of an active harbor would definitely be contraindicated.
But as stated above - a 200 year old wreck doesn’t look like an intact ship sitting on the bottom of the ocean, with the name “Endeavour” clearly showing on the stern. It’s undoubtedly a jumbled pile of old planks at best.
If any ship was important enough to have been preserved in British history it would have been the HMS Bellerophon. She was a British 74, the backbone of England’s “Wooden Walls”, and was the only ship to have been at the Battle of the Nile, Trafalgar, and the Glorious First of June. She was the ship that Napoleon ended up surrendering to. Was she saved? Nope. She was put up in ordinary, converted to a prison ship and then finally sent to the breakers yard. History and tradition may be important to the Navy, but not, apparently, sentimentality.