YANBU - but - I'd let her have a phone.
My son got his the Christmas before he went up to secondary school, aged 10. Before then, he had one of my old phones, without a SIM, linked to my Apple account so he couldn't purchase anything. Now he has a proper phone, we use the Family Link app - he can't access YouTube on it, he can't install anything without our permission, we can remotely lock it/control the hours he uses it. It's really good. He recently made an error of judgement on Instagram, so we've removed the app from his phone, and he's cool with that. He knows it's to keep him safe, and that the phone is a privilege. He also knows that if I ask, he has to unlock it and let me check out his messages. They are all utter drivel - but it's part of the deal that I get to look, for now.
Your daughter asked beautifully, and she needs to learn how to navigate the digital world. It's really easy to place limitations and restrictions on a phone - easier for me to get my head around than the equivalent on a computer.
Of all the social media sites, Tik Tok is the most 'pure' in terms of it being largely just daftness. It has a good heart - but obviously there are risks. You need to understand it, and you need to understand how to keep your daughter safe. This is a reasonable intro: slummysinglemummy.com/2019/12/04/tiktok-a-guide-for-parents/
She doesn't sound phone obsessed. It sounds like you could give her a phone and take it off her/deactivate it at bedtime, and enjoy Tik Tok together. It is much more fun and creative than YouTube, which is the devil's own cesspit and yet we all let our kids watch it on the smart TV and tablets... I'd be refusing YouTube before refusing a phone.