Keeping something sounds like the smaller job, and sometimes it is. What decides it is not preference but geometry: whether the element being kept can be separated from the work around it without damaging either. That question has a clear answer for every fixture in a bathroom, and it is worth asking before a scope is written rather than halfway through a strip-out.
Some things keep well. A cast-iron tub in sound enamel is better than most of what replaces it. A subfloor that is flat, dry and solid is worth building on. A recent toilet, a window, a vanity carcass needing only a new top, a floor that is level and continuous under walls which are not moving — none of those are a compromise to keep.
The difficulty is the elements that lap each other. Wall tile above a tub sits on board that stops behind the tub flange, and the tile itself laps that flange. A failed surround cannot be removed with the tub left in place, because the bottom course will not lift off the lip without breaking the seal that made the assembly watertight — and where the grout at that joint has cracked and the board behind is soft, the surround has failed whether or not it looks it. "Keep the tub, redo the tile" is therefore usually not on offer. Putting the same tub back costs more labour than setting a new one, onto the same ageing waste connection. A tiled shower base has the same relationship with its walls.
What stays needs protecting properly, and a drop sheet is not protection. A retained tub takes a rigid fitted cover, because a dropped tile chips enamel and enamel cannot be patched. Drains are plugged before demolition so debris never enters them. A kept tile floor gets hardboard over the whole traffic route. A vanity that is staying is usually safer removed and stored than defended in place.