Shredded cardboard mulch

My preferred mulch is living mulch. This works great for me. I grow lots of different plants a lot closer than is recommend, and for the most part get great results.
The problem with this method is early in the season there's a lot of exposed soil, and even in the spring the soil dries out fast.
I always struggle with what to use. Everything that goes into the garden is organic. Besides bagged organic compost I can't get any organic mulch. Not only can I not find organic straw, it's kind of scary.  Rice hulls, pretty inexpensive, but not organic, and so light they may blow away.  Wood chips, the kind you buy not organic, costly, and a lot have dies, and who knows what else. The free wood chips I get from my local tree service, are also scary. I don't mean to be paranoid, but people spray and use systemics, and weed killer, and all kinds of stuff I just don't want in my garden. I haven't saved leaves, don't have a cheap source for wool. Chop and drop breaks down pretty fast, so I think it's great for adding organic matter, not such a great mulch. My grass are weeds we mow and pretend is a lawn, so I definitely don't want that in the garden.
Shredded cardboard. I have an abundance of it, and  it's free. It's not organic, but it seems relatively harmless as long as I don't use the cardboard with colorful graphics. 🤔
I've tried to find information about using shredded cardboard as mulch, and didn't find anything. I found people using piece of cardboard, which seems like a bad idea because water doesn't penetrate the cardboard.
I have decided to give it a try on a couple of my beds I planted late. I have a 15 page paper shredder. It's not fancy it cuts small stripes, and works great on cardboard. I soaked the shredded cardboard in water for a bit. Watered the bed, and spread the cardboard on about 1 to 2 inches thick, except in an couple of places I planted some seeds, there is a very thin layer.
It's only been a couple of weeks for the first bed and a week for the other two. So far I'm very happy. I don't know if it's a coincidence, or because it retains water, or the roots are cooler, but the plants are really taking off. It's great for the little seedlings, before when I would water the soil would cover the leaves. The cardboard prevents that from happening.
On the first bed I put in 1/4 soaker hose. I wound it around the plants, then the shredded cardboard covers the hose. This way I can water everything in the bed at once. I hope it will save water and time. The problem with soaker hose is I have very hard water, and it will plug the hose up. That's why I went with the 1/4", it's cheap so when it clogs up I won't feel to bad. I'll use it to tie up plant, or something.
It's still early, but so far so good. This may be my go to mulch. Time will tell.

We shred all of our cardboard and the 3 neighbors give us all of their boxes to shred. Like you mention, we exclude anything with a lot of ink or gloss.

The shredded cardboard goes directly as mulch or into the chicken coop to get made into compost by the chickens. My initial concern was that it would blow away but once it gets wet, it seems to stick together well and hold together.

It is a great alternative and we have been happy with the performance so I second this as a good option.

I keep meaning to run rolled up boxes through the chipper shredder -- as much as anything to see what comes out, but I get it out and fire it up so infrequently that it hasn't happened yet.

It's a strange coincidence, but it's been exactly 2 months. I have interesting results. On the bed that has the soaker hose the shredded cardboard works great. I didn't have to water as often and everything in that bed grew very well. The only negative for this bed was totally my fault. Twice I forgot I was watering, and watered for about 24 hours. Luckily I only lost one plant.  The beds I hand watered didn't work as well.  The cardboard tends to work it's way into the soil and disappear pretty quickly.
So at this point I've learned if I use a soaker hose shredded cardboard makes a great mulch. If I hand water, I will have to use it in the beginning, and plant living mulch, or keep adding the cardboard.  All in all I'm happy with this little experiment.