Are there shipwrecks full of loot in the Mediterranean Sea?

No, because loot implies plunder and materials taken with intention to sell. There are however, a substantial number of wrecks containing valuable artifacts with significant cultural heritage. Looting is very bad for many reasons but that is another discussion. If you're interested in learning more there are about a dozen archaeologists here who would be happy discuss why treasure hunting is bad for cultural preservation if you want to post another question.

Now onto the meat of your question.

However would there not be a greater concentration of shipwrecks in the Mediterranean relative to it's size?

The concentration of shipwrecks in the Mediterranean is very high as you suspect. People have been actively sailing roughly the same trade routes for thousands of years resulting in a larger number of wrecks than the Americas. There are also ancient seafaring traditions in Northern Europe and East Asia so there are many wrecks in those locations as well. These areas are less well documented so it can seem like there are fewer wrecks. The notion of a higher concentration is somewhat deceptive because oceans also experience areas of vast concentration. The Outer Banks of the United States is part of what's known as the Graveyard of the Atlantic because of the large number of wrecks there.

Most shipwrecks occur close to shore. Many ships sail within site of land for navigational reasons or to take on supplies. Ships can be driven ashore by storms that catch them unprepared. A ship in peril will often make for land in the hope that the crew can escape. Shallow water close to shore makes hitting rocks and obstructions more likely.

All of this results in specific locations in a given body of water developing a large number of wrecks because they are dangerous. Sometimes they even pile up on each other. This means that while the Mediterranean does experience large concentrations of wrecks it is not alone in that fact.

The entire sea floor is also not covered in wrecks. While ships are big compared to people, compared to the sea they are tiny. The vast majority are small vessels less than 100 feet (30m) in length. So while wrecks are common in the Med, and the clear water means even deep (relatively) wrecks can be seen from the surface its not as if they carpet the bottom.

why do people not salvage these?

Before the advent of SCUBA (Self Contained Underwater Breathing Apparatus) gear underwater salvage work was difficult and dangerous. It still is. A diver recently died working on the Costa Concordia. Before the invention of SCUBA the main underwater workers in the Med were sponge divers. By 1900 those who could afford it were using surface air supplied diving suits with copper helmets of the kind you are familiar with from the movies.

The most common artifact of value on Mediterranean wrecks are amphora, clay vessels used to transport wine and other goods. They survive quite well and frequently form piles which are the only visible portion of a wreck where the wood has long rotted away. Well preserved piles sometimes even retain the shape they were stacked in in the hull of the ship. Frequently the only surviving wood from the hull will be buried under the amphora pile. Prior to the 1950's relatively few were salvaged because they were common and not very valuable. Few outsiders were interested and the locals could not usually get a good price for them so it was not worth taking time and cargo space that could be better spent on sponges.

That changed in the 1950's and 1960's when SCUBA became a popular sport. Suddenly vast numbers of people were underwater as tourists in what had previously been a specialist's realm. Amphora and ship bits became popular souvenirs. This caused a large number of shallow wrecks (those within about 100ft of the surface) to be thoroughly looted by the unscrupulous and the ignorant. Local divers also sometimes salvaged ship pieces and cargo to sell to collectors. Peter Throckmorton observed all this as early as 1970 in his book Shipwrecks and archaeology; the unharvested sea., which is a plea for protection of wrecks and archaeological investigation thereof. The book is somewhat dated now because the value of underwater archaeology has been much better established, but it is still an interesting look at the infancy of the field and its state in 1970.

In more recent times wrecks in the Mediterranean have come under legal protection from the countries there. Antiquities smuggling is a serious crime if caught. That helps, but it doesn't deter all treasure seekers. Those found conducting unauthorized "archaeology" are subject to arrest and their finds to confiscation. Some countries like Greece and Turkey consider any antiquities found within their borders and waterways state property.

Are there shipwrecks full of loot heritage more interesting than amphora in the Mediterranean Sea?

Yes!

Some fabulous artifacts have been found through the years in Mediterranean wrecks. Amphora are very interesting to archaeologists and can tell us much about past customs but they aren't very striking to look at.

One of the wrecks Peter Throckmorton covers at length in his book is the Antikythera wreck. This wreck was found by sponge divers in diving suits around 1900. The wreck was at the extreme depth range for them but when they found beautifully preserved statuary at the bottom they coordinated with Greece to recover them. Here's an article with some video of some of the finds. The most interesting of the artifacts recovered is no doubt the Antikythera mechanism. The device was encrusted with concreted sand and puzzled scholars for many years. After being examined in more detail recently current theories are that it's a computer for use in astronomy.

One of the other fascinating finds discovered in the Med is the Athlit Ram. Until just recently it was one of only a handful of ancient rams that have been discovered. No wreck of an ancient trireme has been found yet so far so these rams are one of our few sources of insight into warship construction other than paintings and verbal accounts. About a year ago almost a dozen more were found! It's very exciting for underwater archaeologists.

People do try and salvage shipwrecks in the Mediterranean. There is an abnormally high number of potentially valuable sunken ships in that area, given its long history of being sailed. In the context of the Greek shores, described above, government regulations have banned salvaging activity. This creates problems when the items can be of significant historical or archaeological value.

Elsewhere, and historically, salvaging was legally more permissible, as an incentive to ship owners and to raise profits for the whichever government had jurisdiction.

But yeah, this might be better in a different Subreddit, though I guess it's about something has significance to historical studies.

Stratification and contamination in ancient Mediterranean shipwrecks is another interesting look at the archaeological aspects of researching underwater ancient sites, but it's more about archaeological techniques than the specific sites and shipwrecks of the Mediterranean themselves.