Why does a bathroom exhaust fan matter so much in a renovation?

Because it is what decides whether the new tile, paint and cabinetry still look new in three years. In a humid climate an undersized or unducted fan puts moisture into the drywall and the framing, and the result shows up as peeling paint, dark grout and eventually mould behind the wall. Size it to the room, duct it outside rather than into the attic, and run it for twenty minutes after a shower. A timer switch is the cheapest upgrade in the whole room.