Barred Owls and Great horned Owls generally do not nest in boxes. Barred Owls are actually quite tolerant of humans.
The species of owls that commonly nest in boxes here east of the Mississippi are Screech Owls and Barn Owls. Most places in the east also have fairly good population of Long-eared Owls, and Saw whet owls. Both of those are not known to nest in boxes.
In the 9 years I lived in South Florida, the Burrowing Owls were the most common by far. We helped the city of Cape Coral do a Burrowing Owl survey every 5 years. Total burrow counts ranged from 1,900 hundred to 2,200. About 800 or so Owls lived in Cape Coral as one pair uses several burrows in raising their families. Burrowing Owls live about 9-13 years and are cute as the dickens. They ate frogs, tree frogs, lizards, anoles, insects etc.
I am fearful as to what impact Hurricane Ian had on them with 7-9 feet of storm surge. They typically start nesting in late January and early February with young owlets appearing in early April. My goodness, I hope that many escaped.