I'm wondering about an alternate strategy for weed / covercrop management, and want to know if I am missing something. I have always heard that you should weed or mulch your gardens because weeds will compete for (1) sunlight, (2) water, and (3) nutrients. I think that there might actually be important benefits from "weeds" in each of these categories, and that the competition during the growing season could be easily managed in favor of your desired plants. So no pulling weeds, and no mulch to prevent weeds, but downright encouraging them as a perpetual cover crop.

(Even though I think they might be helpful, for convenience I'll keep calling this random hodgepodge of plants "weeds".)

1. Sunlight. If you kept weeds trimmed so they were shorter than your desired crop, they would not compete for sunlight. However, if they are kept short, they would still provide shade for the soil, which would help retain moisture. In addition, if you de chop-and-drop, you've got additional mulch during the growing season to further assist with moisture retention.

2. Water. As you trim the weeds, they would have root dieback, and after decomposition of the roots you have soil with more organic material and more structure, to better hold water. In addition, as mentioned above, there are other benefits weeds could have for water retention. With no-till strategy, the continuous presence of weeds would help the soil improve more quickly than just garden plants alternated with cover crops alone.

3. Nutrients. If you are doing chop-and-drop with the weeds, they will not be removing any nutrients from the cycle of your garden -- just tying some of them up. If you have adequate mineral etc. nutrients this will not be a problem -- and the fact that you essentially have a continuous cover crop will significantly help the tilth of your soil, and if you've got nitrogen fixers like clover or legumes as weeds, they are actually fertilizing the soil.

Am I missing something, or is this worth a shot?

You're right on essentially.

What I'd add though is that your definition of a "weed" can be narrowed and designed.
I use radishes, turnips, and peas for filler early in the season before most true nuisance things sprout.
I chop/drop as I want, harvest some, or leave some for seed.

As the spring gets warmer I maybe have one or two solid "weeding" sessions of chop/drop or harvest, plant my major garden crops, and add mulch like leaves/straw/wood.

Then I fill spaces with beans, more radishes, lettuce, or whatever I can find.

I'm now going to try things like sorrel and clover as perennial mulch sources, other things like rhubarb, burdock, comfrey, sunchoke, and nettle can be harvested away from the garden area and used as green mulch to mix with woody things.

I'm reading this convention ag study that shows weeds are the worst detriment in the first part of the year, so like 2, 3, 4, 5, 6 weeks in the spring when plants are establishing. After that it's less of a big deal.

https://books.google.com/books?id=LUSC9lT5Q8IC&pg=PA452&lpg=PA452&dq=evidence+of+weeds+affecting+yields&source=bl&ots=k-Czqot2lx&sig=ftXSn2jL3-obetiCIcs4XnAFVFo&hl=en&sa=X&ei=JBYTVea7Dcq4ggSFvoOQAw&ved=0CF4Q6AEwCQ#v=onepage&q=evidence%20of%20weeds%20affecting%20yields&f=false

So much room for variation. What weeds? Some are arguably volunteer crops and all kinds of helpful, including edible. Others can and will climb your desired crops and drag them down.
Personally I really like Mike Pilarski's approach. Get photosynthesis happening everywhere, and get your preferred plants so well established that the weeds in your gardens are your own hyper successful plantings from prior years.
But, short answer, yes "weeds" can be beneficial.

the only time I really pull 'weeds' are when they are right next to another plant and I want the other plant to be growing well and not the 'weed' I also toss seeds all over my garden so that things grow where they want to grow. it is very wild looking but it seems to be working really well even with my fairly poor overly acidic hydrophobic soil. I like the weeds for holding down the soil and providing shade and when i do pull weeds they just get turned upside down so the roots dry out and they become part of the mulch. I do make some extensions and occasionally go more extreme with weeding out poison oak which I and none of my family are allergic to but I don't want visitors to get a rash and also english ivy which is pretty invasive here and problematic in some areas.

my goals are like what Peter said. I want to get my favorite plants so well established that there is no space for the poison oak or english ivy to be a problem.

Good discussion I like the radish suggestion.

I would add to consider the soil PH situation - I've found self planted 'weeds' are growing in a spot for a reason, you add mulch of any type, chop 'n drop, or other amendment and your changing the soil ph.
This is good, but over time you may find your dandelions (for tea and wine) disappear in favor of some grasses or ..... some other unexpected change over.

How this goes depends on what your calling weeds and what those weeds need and like to continue in a specific area.

I like how the weeds help me to know what the ph is now and how they help me to watch the ph change! my soil is too acidic for a lot of plants so seeing that change in places is neat and exciting!

Bioshelter market garden. Darrel frey. He has established and selected native edible weeds as cover crops, sells for 14+ us dollars per pound.

The one important thing about living mulches, opposed to a chop and drop, or crimp kill, is; living much systems require deep watering. Otherwise you get a great dense weed, but water lacking produce. I'm not saying this is applicable in all spaces, but definitely something to encourage, if you get weeds that need removal, making a profit, or meal, is a nice exchange for our labor.