I've done intensive double dug gardens, I've done single dug gardens, and I've done no dig. Quite a few gardens of each kind over years in many different places, so I think I have pretty good experience to speak from. I never much liked the idea of raised beds in boxes because I'd rather work with the soil in the ground than constructing something to hold a bunch of "garden soil" from a hardware store. I did hammer together some boxes from scrap wood once and fill them with raked leaves and compost and used them to grow quite a bit of veg, mostly greens, but that was when I was between places and only had an asphalt alley for a growing space. As a last resort. If there's in ground space available, there's no need for a raised bed, and yes, I've worked with really heavy clay soil. It has potential, just have to develop it a bit.
Anyway, in my experience, double dug beds aren't worth the work. It's like the marathon run or English channel swim of gardening. Bragging rights for over achievers. Or masochism. I never noticed any real increase in what grew from a double dug or once dug garden.
No dig, as you've commented, often inspires people to put all sorts of plastics on the ground to shade out weeds and prep the area. When I tried no dig, I used a heavy canvas tent tarp with an old door I found on top of it for weight. Didn't leave a bunch of plastic in the ground. But even though, it wasn't a roaring success. It seems to me that even when weeds/grass have been shaded out, the ground still needs to be opened up and folding in some nice organic matter certainly helps. It doesn't have to be fancy... A few bags of raked up leaves mixed with a bucket of manure of some kind makes a decent nitrogen/carbon mix without getting all geeky about the exact proportions. Horse stables are a great place to get free manure (besides chickens of course). When I lived in cities, I would just go to the stables where the mounted police horses were kept and shovel a few buckets for free.
The other problem with no dig is that a lot of people just don't seem to realize that for all that carbon heavy stuff (wood chips, straw,etc) takes a loonnng time to become a decent growing medium. Like at least two years in a temperate climate.
I always got the best results from a happy medium: by digging to the depth of most garden plant roots (6 inches or so), folding in manure and raked leaves, and mulching over.
And the best time to do this for a really thriving garden is not in the early spring -- it's the late fall in prep for the next spring. Time and microbes work wonders.