Beneficial weeds - what roles do creeping annuals fill in an ecosystem?

I've created a bit of a project with a friend out of putting together an informational document on 'weeds that you might want to cultivate a relationship with' (instead of pulling just cause they fall into that weed list). And on this list is cleavers and chickweed, of which there is plenty of information on uses for both, but I'm looking for resources or information on the kind of niche that these and other other creeping annuals fill in an ecosystem.

I'm open to anything that can be said on the matter.

Living mulch and roots to hold soil in place.  Organic matter added to the soil.  I think a lot of people here use them as animal feed if they don't eat them themselves. Pollinator and other beneficial insect atracttor.

If it's not uncomfortable under the feet or specifically causing problems I tend to ignore most wild annuals.  I need a reason to do the extra work. We're pretty good at identifying our weeds at very small seedling stage.  Wild sunflower is welcome in all the flowerbeds, well do we really need to walk there if it's in the lawn. Bindweed, better get that ASAP before it starts choking the other plants.  

In my area, chickweed grows well in spring and dies back about the time that I plant summer crops, so I let it grow as a cover crop. It provides shelter for small insects, supports soil microbes by having living roots in the ground, and leaves behind organic matter as it dies.
Cleavers are a different story. I suppose they could have the same cover crop benefits of chickweed, but I can't stand how sticky the big patches are.