I don't know how common it is to own your living space in the US, but where I'm from, it is fairly common. And I don't think "how expensive per square foot" is applicable when you aren't renting.
But either way, you won't be paying more in rent and/or utilities for having an extra box in your closet.
Unless that one box is the one that causing you to buy/rent more space to store things. In general storage space is very lumpy - people have a fair amount free until they don't and need to get more space - when you get more space you tend to get a lot more. (Of course downsize/decluttering is also an option)
But either way, you won't be paying more in rent and/or utilities for having an extra box in your closet.