If you want to look at it from a matter of practicality, they don't have the means to keep that thing in usable order indefinitely. Look at their architecture, they're not about and might not even know the large scale metallurgy required to keep that thing standing long term. It's better that they scrap it and re-purpose the metals towards smaller smithing projects in The Yard and then build up their own lighthouse rather than put effort into upkeep a symbol of their oppression just because it serves a practical purpose that could done with less trouble or be a constant, looming symbol of an attempt to erase their culture.