From experience, I can say that finishing a metal or welded staircase frame with wood is not very durable. No matter what type of hardwood you use, after a while, creaking and loosening begin, and the treads begin to crack. This is due to the difference in materials.
The metal frame is always cold, while the treads are warm. Furthermore, when climbing, the staircase always "breathes" slightly by a few millimeters, and this is enough that after a year or two, the glued joints begin to crack, and the screws and various metal fasteners begin to loosen. As a result, the staircase wobbles and is terrifying to walk on. Eventually, everything falls apart.
Furthermore, a properly welded frame is essential. Welding experts fail to consider the dimensions of the risers and the gaps between the treads. A welded structure may look good and sturdy, but when finishing with wood, all sorts of unaccounted details come to light: the width of the treads at turns, the overlap of the risers in the narrow spaces of the turning steps, etc. On porches or small rises of 2-3 steps, this isn't noticeable, but on flights of stairs 2 meters high, it's noticeable. Therefore, the welded structure almost always has to be dismantled.