I'm thinking that most nitrogen fixing trees could be managed as coppice, and many vegetable crops can use some shade in hot climates (even peppers and eggplant) so sun competition would not be severe. The nitrogen fixation should help avoid nutrient competition. Water competition would be an issue, but irrigation could be increased, and in any case, the tree sprouts might slow the wind, and create a shaded, moister, calm environment, slowing evaporation.
Spading or forking could prune the roots, keeping them below the level of the vegetable crops.
I have just by chance a large alder right next to my veg garden, (double trunked each trunk over 18 inches) it's on the northern side so doesn't block much light, only after around 8pm in the summer. Plants growing close to it do worse than those growing away from it, nothing grows right under it. However on the other side of it there is grass, and that seems to do slightly better near the tree than away.
At my place, I don't like trees to be anywhere near the annual vegetable gardens. They really sap the available moisture and nutrients from the garden. If I grow a crop near trees it is bulbs, perennials, shrubs, woody vines, etc. So things like bunching onions, leeks, mint, oregano, sage, raspberries, currents, mushrooms, grapes. Winter crops like spinach, mallow, chickweed, or bok choi can do well under trees if planted around the time the leaves fall, and harvested about the time the trees leaf out.
I think this would work well in forest gardens. Both annual and perennial areas. I have trees and annual crops growing together, you do have to organic material compost or mulch more often in my experience. We seed annuals under our trees all year round, and we have annual and perennial ground covers and understory type canes and berry bushes in the same swales and mounds as nitrogen fixing trees such as black locust and mimosas.
Keeping the nitrogen fixing trees topped short is sometimes necessary to regulate sun exposure.
Check my Instagram for pictures of us planting garlic around our figs and such.
Common Weeds And Wild Edibles Of The World (HD video)