within a century the golden gate bridge would fall into the bay. Especially things by the sea get corroded away incredibly fast, especially metals from the ocean moisture in the air.
In 1000 years, It is a 100% chance that every single metal structure that is held up by said metal will be gone in 1000 years without maintenance. Something like the Empire State building, which is largely comprised of Limestone, would be a a giant rubble heap as it would not withstand the weather and earthquakes that inevitably would occur over time. Metal especially just doesn't last unless under the most desiccated of conditions.
They are CONSTANTLY maintaining structures like the Golden Gate Bridge, going so far as to paint it from one side to the other and when complete they do it again just to add a layer to protect from the elements the ocean air brings.