This wreck was featured on an archeology program in the UK and footage shows very little of it remains. Its mostly cannon and cargo lying on the sea floor. The cargo was construction stone so lots of big blocks of stone sitting around on the sea floor. Very little wood wreckage seems to still exist.

So they can bring up stuff like the cannon but when it comes to the wreck itself there is nothing to raise and nowhere near enough to reconstruct from raised bits of it.