I did not request a laptop but was handed one last year "just in case I want to check on my emails when I am away from the office." When I fell ill, I asked to work at home because I had the laptop but my manager denied my request because I did not have a prior authorization (essentially paperwork) to work from home.
The purchase and issuance of laptops and physical workplace policies need to be evaluated for consistency. It is senseless to purchase extra laptops and issue it to people who do not work at home. If people have laptops, they should be able to work at home in unexpected situations (such as an illness) instead of having to fill out a form ahead of time. Not all things are predictable.