the benefits of green manuring are not only from nitrogen fixing of legumes. the greens are beneficial also as biomass, buckwheat, rye etc. also root crops are used to break soil and bring up deep nutrients, mustard, radish. i use a clover mix (some times marketed as tree and vine mix)
in all my paths and mow it and let it lay as mulch. i also cycle in fava beans, peas and beans in sections whether i want to pick them or not.

The only disadvantage I can see from green manure is tilling it in if you don't have the right equipmnet. All my area is in raised beds, so most power equipment doesn't work very well. I use hairy vetch because it doesn't need to be tilled in. I plant it as soon as a bed becomes vacant (Aug or so), by the tail end of September most of the beds up and growing vetch. If we have a mild winter and good snow cover it will continueing growing in the spring. I have planted tomatoes directly in to the vetch and used it sort of as a living mulch. On the beds with my warm weather crops that don't get planted until late May I leave the vetch on till just beore I plant. It very easy to pull out leaving most of the roots in the soil. Some beds I leave all season until after it blloms and dies back. The dead vetch is also a great muclh just as it is. It reseeds itself very well, so I seldom have had to purchase seeds. I have tried rye and alfalfa, but they are too tough for me to dig in by hand. On the other hand I live on a dairy farm so I have access to tons of bedding and manure, so I have been too religious about green manure.