What are the disadvantages and open challenges of digital credentials in the SSI model?

They cannot simply be used for authentication, they bring high complexity and new technology that every relying party must adopt, they shift responsibility to the user with no central help desk, they run on insecure smartphones, and trust and governance still have to be established.

• Not directly an authentication method: a credential proves attributes ("is over 18", "has licence B"). Logging into an account repeatedly is a different job that classical protocols do well.
• Complexity and new technology: every relying party / verifier must adapt its systems. The implementation effort and cost are still unclear.
• More responsibility for the user: lose your phone and backup, and your credentials are gone. There is no central point of contact that can just reset things.
• Insecure platform: the wallet lives on a smartphone, a device exposed to malware, theft and outdated software.
• Trust and governance: someone must still decide which issuers are trustworthy, how they are registered, and what happens in disputes. Decentralised technology doesn't remove that question; it just moves it.

Go deeper:

• Self-sovereign identity: Concerns (Wikipedia) — semantic confusion, digital literacy and other criticism.