1- The pot.
The pot is without any question, the one item our specie uses to cook, transport and boil water. The pot has a long history, and has been a necessity for aeons. Being able to cook or boil water for more than one individual is primordial. Accessorize it with a wooden spoon, and you have our number one tool.
I think the knife, in most circumstances, is the absolute Number One Tool and at times, the Number One Weapon if it gets bad enough.
I do like where you are going, however.
2- The wool blanket
There is not one refugee or one homeless that does not have a blanket of sorts. The blanket is what separates us from the element. It simply regulates our body temperature. Blankets go way back, and our ancestors regarded them as a necessity that became sacred...the blanket is our cocoon, it allows us to rest, to isolate ourselves physically and psychologically from survival itself. It gives us comfort and security.
I think a surplus USGI wool army blanket is something to behold, indeed.
3- The tarp.
Although a more "modern" tool, the tarp has made it to the top of the list. A tarp is one of the most iconic symbol of refugee camps and homeless around the world.
No, Buddy, the tarp is not modern. The materials might be, but the tarp goes back to cavemen using animal skins and lean-tos when they couldn't find a cave to inhabit or whilst traveling.
You are correct that it is a must-have item, however.
4- Water.
This realm is as we all know beyond a necessity. The jerican is as iconic as the tarp. A means to store and carry water is life. A jerican coupled with the pot, and you have survival. Ken mentioned the collapsable ones, which is a good option, but i am partial to a solid jerican for further transport possibilities and durability.
If you have a way to actually transport it or you have collapsible versions for water transport, absolutely. This, strangely enough, also goes back to animal skins as the tarps above.
5- The machete.
We can talk long and hard about the knife, but when it comes to survival at its core, the machete has proven to be an amazing asset.
The machete is in use all over the world, it provides an extra "edge" over the knife, because it extends the possibilities around camp. A machete can chop wood, and stir a fire, it provides further reach and is a tremendous defensive weapon.
From Africa to the far East, from the jungles of south America to Asia, the machete has risen as the survival tool of choice.
A lot of people who are experts at jungle survival would absolutely agree with you, Jeff Randall and Mike Perrin of ESEE Knives (Formerly RAT Knives) would be two people to agree with you. The peoples of Mexico, Central and South America, Africa and Southeast Asia all would as well.
If I had to have only one edged tool, it would probably be a machete but not the big barracuda types but a smaller 12-14 inch bladed machete.
6- Fire.
What can we say, about a realm so abstract and yet so grounded as fire ?
Pot + water/food + fire = survival.
Fire is one of those necessities that Man had to master. Fire itself, has influenced our evolution. That alone should remind us the importance of this realm.
It can keep you warm.
It can cook your food and make it safe to eat.
It can boil your water and make it safe to drink.
It might keep animals away at night, I'm not convinced of it, but it cannot hurt, either.
It can be used to signal for help.
It can keep insects away that make you miserable or sick with disease.
I find nothing to really disagree with when it comes to fishing, which I think is one of the most underrated survival skills and I think some people who actually hate fish and refuse to learn how to fish might get really hungry and possibly starve.
First Aid Skills and other, peripheral skills are a must and the soap angle is very, very important.