AITA because I will not let my daughter have a second phone for social media?

My 13 year old daughter has been begging me to let her get an extra cell phone which she will use only to share with social media. She says that her main phone has all of her business on it such as her email, social media, online schooling, and texts. She claims she took pictures of a really cool sunset and only realized later that it had a bunch of rooftops in the foreground which she didn’t notice in the moment and didn’t want to take again. So she’s saying that with a second phone she can have just a little camera phone that she can carry around that is completely unassociated with her identity, and that way she doesn’t have to worry about the inconvenience of accidentally taking a bad picture and having to redo it, and she also doesn’t have to worry that she’s accidentally posting her personal location. I think this is a lot of money for something silly that she doesn’t need. She thinks it would be fun but I just think it’s unnecessary. She is researching used phones and has found a really cheap option but I still don’t want to spend the money. So I am an AH for not letting her have a second house for social media?