Mother Nature never developed a long distance surface swimming animal - all animals swim below the surface or fly in the air, they avoid the violent layer where athmosphere and ocean has this violent interchange called waves, the water surface is a biological desert - even whales which started as a land animal breathing air are now swimming below the surface.
There are good reasons for this - the drag below is a factor 5 lower and the submarine ambient gives protection and constant buoyancy.
Submerged protection - how deep must a structure be submerged to be protected from waves?
When talking about protection from wave damage we should have clear that one thing is being protected from wave hazard and sea sickening movements what happens inmediatly when you are submerged - and the other thing is how deep in the ocean you might notice the pass of big waves.
Wave hazards come from 2 factors:
1) breaking crests that can hit a structure with hundreds of tons of force
2) Hog and Sag, bending and torsion, forces which appear when a ship is supported by water (and bouyancy) at one end and in the air at the other end. Those forces can break a ship or lead to fatigue. They make a ship stamp and roll.
If you leave the math and wave amplitude thing apart, you can easyly understand that neither wave crests nor hog and sag can exist anymore as soon as you have a thin water layer closing above you, even when this layer is just a foot deep. The structure will be supported uniformly by water at its whole length and this uniform support leads inmediatly to a much calmer behavior.
This is what a diver experiences when he jumps from a rocking surface boat - there is inmediatly this incredible calm uniformly supported floating status when you go below the surface it dos not start gradually dozends of meters down - it is just below the surface. No wave is HITTING you anymore no wave is pushing you and your equpment around as it is the case when you swim on the surface. The only thing you experience below is a kind of current that changes direction with every wave. So you can "percieve the wave movement" when you have a visual reference to the sea bottom. If you don`t have this visual reference you will not notice the movement.
I know a lot of divers that are suceptible to seasickness in a rolling diveboat and they are always the first to jump overboard - once you are below seasickness is gone.
I experienced this in extreme form at Malpelo Island which is a island in the pacific 500 km off the coast of Colombia between Cocos and Galapagos - you have those real big pacific waves comming in directly towards a volcanic rock face. There is no doubt that any ship no matter the thickness of its steel plating would be hacked to small pieces within minutes. The divers jump overboard far from the rocks and swimm below the surface directly towards this rockfaces - this is where all those beautiful fishes are. You hang there 1-2m below the "hackzone" relaxed enjoy the smooth waiven of the waves comming in, you can feel the real big suckers in your ears, as the waterdepth changes while the crest goes trough. It is a wonderful place to mediate about the fact why nature never developed a surface swimming animal for the open sea - maybe living below is just so much better.
The other experience i can contribute is the experience i had with the submarine yacht prototype - while i had the sub on its anchorplace and was tooling around inside i closed the hatch to avoid questions from courious visitors - i was there for an hour or so and when i opened the hatch i noticed that a storm had come up, several trees felt down, sailing yachts in the 30 foot range where calling SOS, and the local rescue crew was busy to assist. - I did not even notice the storm. And the hull was still on the surface exposing the sail (tower) and the central rounded part of the hull a bit above the surface. Obviously this did not present enough wave and weather attack surface to make the hull rock and roll.
The difference between being hit by the waves on the surface and being supported completly by liquid is paramount - this is why whales have structural weak bodies compared to a ship, they can live with a lot less structure.
Modern shipbuilding is including ballast tanks into the design to deepload the vessel when necessary to avoid excessive bending in the violent surface layer and get a more uniform hull support.
The question how deep is deep enough is most of all a practical question - i would say a few feet is enough for leaving your coffee cup on the table in 99% of the sea states you will experience, 10m will be enough for leaving the coffee cup on the table in the perfect storm. What means that there is no need to go beyond a depth where a decent snorkel is still possible.
I know that there are people theroizizing that big waves reach deep down in the ocean - the point is theirs hazardous and seasickening action depends on intermittent air/iquid contacts with the hull - and those are gone inmediatly below the surface. What is left below is waiven that does no harm and no seasickness - any diver can tell you that.