Problem with dry berthing or docking her is economic. Ship itself can survive docking just fine - witness her being currently docked. The real problem is that building a graving dock that size is a billion dollar project, with considerable ongoing maintenance cost. For smaller ships it's possible to find old unusable docks (i.e. HMS Victory) or build a berth (Albacore). Much harder with a big ship.
From a structural perspective, docking entails significant local loads, but the ship is designed for it. Once safely docked, the ship is stable and should be structurally able to stay there indefinitely (assuming dock is structurally stable itself). Wood ships have issues with long term docking, but not steel. This is the result of creep - deformation under extended low load. Steel doesn't suffer this. Wood is also far weaker structurally, which is why it is only with iron shipbuilding that large ships were practical. A wooden ship is generally designed with a pretty even distribution of weight and buoyancy, which results in minimal static stress overall. I.e. each section of ship largely supports itself. That changes with steel - concentrated loads from boilers, engines, armor, gun turrets, etc. and finer hull forms (for speed) result in significant structural loads. In the big ocean liners for instance, stresses of several tons/sq inch are normal just sitting there. Docking eliminates this stress, so you actually have lower overall loads when docked.