As you can see in the pictures you linked, many of those pots are just about 2-3 feet deep, and the same width. What you are proposing to do is totally doable.

I've read that some people did use potting soil and kept it moist all the time in the same way you have suggested with standing water in a tray. Another example I saw was that the person used a kiddie pool. That's about a 6-feet diameter's worth of growing space for your water plant nursery, and the water level could be a few inches up to the full height of the kiddie pool.

The soil substrate he used was then just soil from his backyard.

A final example I've seen is that plants were grown in a smaller container without drainage holes. So the container was not filled with water a la the kiddie pool idea on a smaller scale, but it was only allowed to have muddy soil, or whatever consistency you wanted to grow at. In other words, it was up to you to maintain the water so that it wasn't too soggy or too dry, since there were no drain holes.

I've done this for years, works fine and is great fun. Plants of this type we generally call marginals, grow up out of the water. The other kinds are floaters and submerged. Marginal comes from these normally seen around the edges of ponds, growing on the banks and into the edges...at the margins. Another term and good place to search for marginal plants types is "vernal pools".

I've tried many kinds of plants. I use terms like "crown submerged" which means standing water over the soil, and "wet feet" meaning no drainage holes in pots but no standing water at least most of the time.

In all cases I've found so far the less water the better. You see that with all marginals in mud ponds...as the water gets deeper the plants get smaller and smaller as they do less well until the water is so deep they can't grow. The biggest plants are on the banks, out of the water but with roots going down into the water.

It's a common misconception that these plants "need" to be in water. I think mainly because plant containers and web site will say plant X - 6" of water. But that's the max recommended depth, not a requirement.

This blew my mind when I moved to Phoenix 10 years ago...pond plants are very common in landscapes here...in the desert. Canna, Umbrella and papyrus plants of different kinds, Gaint Reed, Cat's Claw, Ruelia are all very common. Planted as normal garden type plants.

The deal is these plants are adapted to being able to survive in water or wet soil. Doesn't mean they like it.

But growing these in pots with wet feet has advantages. They get all the water they want all the time and watering is easier.

Here in Phoenix the pots themselves need to be shaded else the soil get's in the 120F range and that's problem (they still survive for a long time which is amazing). If you look at vernal pools you see these plants are adapted to living in dry soil for extended periods...like in our desert climate where even watering once a day isn't enough for many plants but marginals can get by.

All so far like likes of fertilizer.

Potting soil imo is bad...really bad. When wet it can produce too much ammonia. Some ammonia production is good, plants love it, but too much and they die pretty fast. Most growers say the soil is "too hot". I like to use clay soil...more clay the better. Then I can control the amount of ammonia with the type and amount of fertilizer. And clay soil is generally the kind of soil these plants have adapted to anyways.

The only plants I've had less luck with are succulents and cactus. They rot pretty fast if their crowns get wet. But many succulents do fine with some degree of wet feet. Haven't tried a lot of cactus because I've seen no advantage...these do fine in normal soil conditions.

To take this to the extreme I've grown Mesquite trees and Caesalpinia mexicana from seed in pots with no drainage, not standing water at least for very long, but wet feet for sure. And the roots down at the bottom of the container were thick and healthy looking. Any expert will tell you these will die without great drainage...but that's not true. What's true is that in this environment a lot of kinds of bacteria can grow that these plants are adapted to and at some point can successfully attack and kill the plant. But I grew these trees and shrubs for several years and they grew fast and tall. When transplanted into the garden they continue to grow like any other transplant.

Do well with wet feet: Tomato, Iris, Calla Lily, all the taro and elephant ear plants, impatiens. But there isn't a plant I wouldn't try. It seems to just be a matter of what level of water they can take.

Many plants don't survive wet soil from seed, or in their dormant state. They need active mature growth to fighter the microbes growing in wet soil. Seeds for example will germinate in water, but if the water isn't changed the microbes will likely overwhelm the young plant. Canna rhizomes can rot in wet soil when the plant isn't growing.