Not true. The device's public key is also sent, which functions as a stable device identifier.
We've spent years trying to get away from stable tracking IDs and fingerprinting. Returning to a system where devices are sending a stable ID to a website to prove ownership is a step backward.
There are proposed mitigations like issuing multiple sets of credentials or rotating them, but we're not going to get an infinite number of keypairs for every website or session in the secure enclave in practice.
Another reason why these proposals aren't getting much uptake is that they aren't addressing what the lawmakers are pursuing: They don't want anonymous authorization tied to the device. They want IDs tied to accounts and a way to discourage people from sharing IDs. In the anonymous systems it only takes one person a few minutes to put an over-18 identity into a device and there's no way to determine if someone is abusing the system by stealing IDs or if someone's 18 year old brother is setting up all of their younger brothers' phones for $5 each.
The situation gets stickier when you acknowledge that it's not possible to limit all of these websites to only mobile phone devices with secure enclaves that are not jailbroken. Once you open a door to desktop devices and other OSes accessing these sites, you open the door to replaying and proxying attacks, where someone will produce those `over_18` attestations on-demand for you, possibly for a minimal price. This brings us back to the public stable identifier to discourage fraud, which means governments won't be happy to issue as many keypairs as we want, which means we're back to semi-stable fingerprints.