Attestation depends on a few things:

1. The website has to choose to trust a given attestation provider. If Open Source Browser Attestation Provider X is known for freely handing out attestations then websites will just ignore them
2. The browser's self-attestation. This is tricky part to implement. I haven't looked at the WEI spec to see how this works, but ultimately it depends on code running on your machine identifying when it's been modified. In theory, you can modify the browser however you want, but it's likely that this code will be thoroughly obfuscated and regularly changing to make it hard to reverse engineer. In addition, there are CPU level systems like Intel SGX that provide secure enclaves to run code and a remote entity can verify that the code that ran in SGX was the same code that the remote entity intended to run.

If you're on iOS or Android, there's already strong OS level protections that a browser attestation can plugin to (like SafetyNet.)