no more weeding the veg garden, without use of ANY chemicals, Mohawk method

I have recently been trying to learn about my native ancestral farming ways and incorporating some of these ideas in my yard. One of the ideas I call "lazy gardening,the no more weeds method with no chemicals". it talks of the women of the Mohawk tribe being busy, not lazy, but this is how I see it, as I have not had to pull a single weed all year long. first remove all left over plant material from all the flower beds, add any sticks and branches from trees in the yard and any dry grass and leaves that haven't yet been used in the compost. have yourself a nice controlled fire, be sure to have the water hose turned on just in case of the fire jumping or trying to spread.(add some extra wood and branches if you don't have enough material to get a good blaze going as you want the heat to be enough to split and open any stray or volunteer seeds) leave the ashes to cool, then mulch ashes into soil. before planting in the spring, once again its time to set fire to the garden. the first fire opened the unwanted seeds, the second fire burns them, as well as rids the garden of unwanted bugs, eggs, molds and fungus. after adding compost, the Mohawk women would plant 3 corn seeds, with 3 bean, and 2 squash. the bean climbs the corn stalks,and doesn't damage the corn plants growth, the squash leaves shade the soil from moisture loss, and fill in the spaces between corn stalks so no space is wasted. by not having to weed my veg garden any more, i have more time for my flower garden and bonsai collection. if anyone has any other time saving ideas for fruit,veg or flower garden, i would love to hear them.