Follow label directions and treat the soil. . The planter boxes attached to buildings are usually a nightmare in one way or another. They are usually under building eaves, so must be watered by hand or with an irrigation system. The boxes often leak into the house. Bug populations quickly build up under the eaves, particularly spider mites.
Plants usually suffer one way or another.
I personally would cover the soil in the box with a weed barrier and put decorative red lava rock or river rock over the weed barrier. Q. You write about invasive plants and suggest removing most of them from the yard. But, some of Florida's weeds are attractive. My tradescantia was given to me by a neighbor a two years ago. You are correct.