An alternative to a wired dongle is a high-quality bluetooth amp, e.g. from Fiio. It's reliable, keeps your phone free from cables, but you can keep using your high quality wired headphones.
Fair, this may be a legal option for ordering alcohol. I really don't see the pure cryptographic hash "is older than 18y" as a big privacy issue though, as long as it is properly salted, does not provide other information on my identity and is unlinkable (i.e. multiple such signed claims are different).
The last time I opened an account for a financial service, as well as when creating an account with a service for digital document signatures, I had to do a video ident process with a private third party company. There was no other option, and I felt quite uneasy about it. I would have preferred the E-ID by far in both cases.
Both companies will inevitably store information about me to provide their service, independently of the identity verification. That is legitimate and inevitable for their service. That other, third party company storing a video of me holding my ID and my face into the camera is now not inevitable anymore.
Quite a few actually do require ID-scan-through-email (which is horrible). Or, they simply delegate to a third party video ident service, often in another country (because cheaper).
How exactly is the status quo not much worse than "I give you a cryptographic hash proving that I am over 18, but nothing else, and without the state knowing that this transaction happened"?
Companies can already request and will still be able to request a PDF scan of your ID. Or worse, video ident through a private third party.
This is the status quo for ordering alcohol online, or if you want to open a bank account.
The new E-ID based on SSI (self-sovereign identity) is so much better than the status quo from a real-world privacy perspective towards companies that must verify your identity or age.
The Swiyu team dropped the Play Integrity requirement on Android: https://github.com/swiyu-admin-ch/eidch-android-wallet/issue... This means that the E-ID will be officially supported on AOSP based secure ROMs like GrapheneOS, without any requirement for Google services.
Keeping the battery charged is a weak point though, agreed.