1) If they break, I’m on the hook for fixing them. Plus, what if for some reason they get injured on them (god knows how).
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FLU, as I understand it, you are typically not required to maintain all amenities that are part of your rental at the start. I.e., if an amenity such as a fan or a gas grill breaks, as a landlord, you can simply elect to remove it. Typically, this does not violate the lease or make the property uninhabitable. Now, in my opinion, I would repair such an item if it had been an amenity when the lease began, but perhaps only the first time (particularly if it was broken by lack of reasonable care on the part of the tenant).
With regard to ceiling fan injury, I managed to slice my fingers up pretty badly when taking a shirt off in a room with a ceiling fan once…