Again Ledger CTO here, yes, we won't use biometrics because the cost to of doing it correctly is definitely not worth the benefits. And when not done correctly, it can create a persistent liability for the user.
Just considering fingerprints, the most common one today : first, you want a good quality sensor to collect your fingerprints (otherwise, this can be fooled by a fake finger, gummy bear or whatever) - most consumer grade products fail right there. Then, you want to connect it securely to your matching logic (otherwise, every malware or physical attack can reveal your digital fingerprints, again, you don't want that to happen since it's complicated to revoke a finger without chopping it off, and a digital fingerprint can be a great way to fake authentication into other brittle systems). Finally, you want a secure, fast and reliable matching logic (secure for the same reasons as before, fast and reliable because the user experience is going to suck otherwise)
Apple actually does most parts right as described in
https://www.apple.com/business/docs/iOS_Security_Guide.pdf - but that's more the exception than the norm, and of course the generic consumer grade sensor is still bad.
The Secure Enclave is responsible for processing fingerprint data from the Touch ID
sensor, determining if there is a match against registered fingerprints, and then
enabling access or purchases on behalf of the user. Communication between the
processor and the Touch ID sensor takes place over a serial peripheral interface
bus. The processor forwards the data to the Secure Enclave but cannot read it. It’s
encrypted and authenticated with a session key that is negotiated using the device’s
shared key that is provisioned for the Touch ID sensor and the Secure Enclave. The
session key exchange uses AES key wrapping with both sides providing a random
key that establishes the session key and uses AES-CCM transport encryption.
You'll have similar requirements for other biometrics - good sensor, secure pairing with the matching logic, secure, fast and reliable matching logic. Also matching logics are complex and highly proprietary, which doesn't really fit that well into Bitcoin decentralized and trustless design either. It's quite difficult to be able to evaluate yourself how snake oilish it really is - for a good laugh, just ask your local fingerprint solutions vendor how the matching algorithm works, or even how minutiae are encoded.