I guess this brings up the question, is it bad to let it go wild? Assuming things will get chopped and tilled in.
Seems similar to green manure, though far less deliberate.
If the wild plants go to seed, yes it can be bad, very bad.
My garden space now was originally part of a hay field over 40 years ago. When I first started trying to grow veggies in it, it was a
nightmare of weeds. My first year I literally lost the veggie crop completely to weeds...and I'm no lazy gardener.
As years passed, I learned that the use of cover crops substantially reduced the weed problem...and other problems as well. Today, that former hay field soil is virtually weed free. It is never ever allowed to go fallow which in my opinion would require starting the whole process all over again... something I have no interest in doing.
Yes, green manure is a good thing, even a great thing in my estimation but if weed control is important to you, then make sure the soil is always under some protective cover crop or producing plants. If you don't mind the weeds, then let it go.