Peramdeath is at sea and not other bodies of water. Peoples main thoughts go to rivers, but what about land locked bodies of water such as lakes and reservoirs? These are much deeper than rivers (usually) and wider, but permadeath hasn't been stated because of that.
Caspian always chooses his words carefully when he says it'll be death at sea, as in he doesn't say "sea" he said deep water. He has described that 2 people could fight in the water and if 1 incaps they will drown and perma-die. This isn't permadeath by touching the sea, it's permadeath by touching the seabed.
Think about that for a second if you will
If you read between the lines, doesn't that mean that the seabed is so deep that you can't get back to air before you die again. You'll keep dying and dying because you need to spirit walk and by the time you come back from spirit walking your body is back at the bottom of the ocean again. Maybe someone can drag you back out, but no, they will perma-die trying to reach you.
The sea is the sea no matter how close to land you are. The sea isn't a river because it is 4ft from land, it is still the sea but you wouldn't perma-die in it because your 4ft away from the shore. So again, reading between the lines, it is the depth that is giving you permadeath, not the sea itself.