They require some kind of strengthening or support. Unfortunately, spiral and other winding staircases are not only problematic in design but are also fundamentally unsafe. This may be an intellectual and physical exercise best practiced elsewhere. Other experts agree. As a consequence, winders are frequently prohibited by building codes.
Safety appears to have been a concern at the outset, since there was originally no railing.
Over time, other problems arose relating to the double helix form. The helix, after all, is the shape of the common wire spring. There is reason to suspect that the staircase may be more unstable and, potentially, unsafe than some realize. When I visited in 1993 my understanding was that it was suffering from the constant traffic. It would thus appear that the Loretto staircase is subject to the laws of physics like any other.