The chinampas worked very well because the Aztecs had a large labor force cleaning their latrines into the lake where it would decompose into night soil and later be dredged up to refill the chinampas between growing seasons.
Once they were built up within the underwater stakes, they planted Ahuejote and Ācātzin trees along the edges and corners whose root systems kept the islands from eroding away.
but very cool when they do exist https://en.wikipedia.org/wiki/Floating_island
https://www.bbc.com/travel/article/20220814-the-floating-hom...
You can have a layer of soil in your floating garden too. You can mix in amendments that will make your soil very light and fluffy. A bunch of empty bottles/jars make a pretty good floating raft that can handle some weight. May not be the best if you have concerns about microplastics in your food, but that is what they've been using here in the Mekong Delta.
I guess the key benefit of this strategy is that the water level is high and the water is nutrient rich? Otherwise it's pretty similar to a standard canal irrigation setup.
It’s as close to an ideal growing condition as pre-industrial societies had.