Personally I think all covers are a waste of time and money.
Mine was stored with an outdoor cover on it for 2-3 years between use by the previous owner. Inevitably, it was to keep it nice while being stored outside and I know he meticulously cleaned it before putting it on. But it caused a lot of damage to the paint it was almost hazy, took me a week and a 3 stage to get it place I was happy. Some of the scratches in the clear coat were too deep to get out and needed sanding but too far for me.
It seems obvious: buy a cover to protect it but unless its immaculately clean the buffeting of the wind will buffet the coverm, rub and push the road grime around on the paint and the cover acts like a huge towel, leaving swirls and sometimes worse damage. If you ever put it under when it isnt perfect those contaminants then embed themselves into the soft cover then scratch the car more. Even if you think the car is perfectly clean it isnt always, its amazing when you use clay and see the amount of stuff you cant see sitting on the surface.
Its a good idea to do a full decontamination if storing it long term is something you want to do. Inevitably, the wind will blow contaminants under the cover and cause damage anyway.
Depends how anal you are, but essentially they cause damage and cost a lot of money so why bother. The car is designed to be outside; I would leave it but check periodically. It's better than spending hundreds on covers that actually damage the car.
For me it only makes sense to cover the car indoors to stop dust etc if your storing long-term; the wind causes a lot of the damage.
The other thing to think about with a half cover is that if it rains heavily and the roof gets wet by water being blown under, it takes a lot longer to dry and saturated roofs arent great either. Unless you have water ingress issues the best thing to do is check the drains and do the usual maintenance to ensure the car doesn't leak.