So Brave would fail when Windows says, "hm, your hash doesn't match any recent Edge version, so you don't get to issue a key signing request to the TPM."
Or it will allow the request but when it arrives at the server as "Windows, non-Edge browser" they'll hit you with the endless CAPTCHAs or just boot you out as a hacker.
It's not the web I grew up in.
It seems to me like you can only guarantee no tampering in an actually locked down system, like modern mobile devices.
You might be able to get around it by finding a zero day in the Windows kernel, but as soon as Microsoft discovers and patches it their attest server will stop providing attestations for devices until they install the OS update and reboot to reestablish a trust chain.