What alternative to a users passwords do you have in mind?

The only other potential cryptographically secure alternative might be a TPM chip, if a machine has this. However since a TPM stores secrets system wide, keyrings for each user seam unfeasible and it's likely less secure since you could just boot into single user mode and get the TPM secrets.

Additionally I tend to not trust the TPM (esp. on Linux), because if one firmware update somehow fails to apply properly, I'll have a far more nastier time (since all secrets are gone) than GNOME Shell promoting me to insert my old password.