You certainly need trees...
I usually try to plant to suit multiple goals.
Like say I want fast shade, and want to see butterflies...
In which case I would plant poplar for tiger swallowtails, and hackberry for tons of other butterflies as well as berries for birds.
And, red mulberry attracts birds, not just for the berries, but also for all the caterpillars to feed their babies.
Then, at my house... I need trees that produce wood that won't rot when I cut down the trees...
Trees like black locust, honey locust, cedar, osage orange, black walnut...
And then... everybody likes fruit...
Unfortunately, most of my fruit trees got sick from the diseases associated with our humidity.
I do have a pear tree that hangs in there in spite of fire blight...
and persimmons and paw paws and the fore mentioned mulberry are growing ok...
of course, there are nice shrubs... like red buckeye, and beauty berry, tall blue berry, wax myrtle...
There's going to be plenty of great plants that you can grow instead of that useless patch of turf.