But that's the key thing about tails. You start it fresh every time from a clean usb stick or iso image.

It's more than a browser restart, it's a complete system wipe every time.

Tails is made on the premise that exactly this kind of trick will occur. Sometimes even persisting between browser restart. For that reason even the persistent storage is very limited. But that's optional and cautioned against for maximum anonymity.

What would be worrying with tails would be if there was some way for some hardware identifier to be exposed. Like a serial number or MAC address. But this kind of thing is exactly what it's made to protect against.