You have garbage men who pull the cans out of the enclosure? We have larger containers and have to separate trash from recyclables and much larger containers on wheels. The collectors won't pick up a conventional trash can, they have to be dumped into the larger containers. Because we have so much yard waste, we pay extra to have four containers, two in the garage so we don't have to go out in the heat or cold, two beside the house. Been thinking of adding a feince to conceal them and thought about a cover, but any enclosed structure will soon have a black widow spider or two living in it, so it will be open. I'll probably have an 8 ft section across the front corner of the garage, and another section going back with about 4 ft of space between garage and fence. I'll have to anchor it well because we have some fierce winds around here. I won't put a floor under it as you have, With rain, that wood is going to go bad fast.
The more I do, the less I accomplish.