Phones and sim cards a lot more temporary than ID cards. I don't know of a lot of theves that target ID cards for their authorization uses. Phones... people will steal those.
You can change it in the app, yes.
> How to issue new key if needed?
I think you’ll have to reissue your ID.
There’s also digi-ID (similar e-signature certificate on a card, but without any ID features), Mobiil-ID (e-signature on a SIM-card, no idea how it works), Smart-ID (in app, tied to secure storage in Android/iOS, cross-signed by the server which is supposed to check the device somehow) and probably something else I don’t remember. All of these are independent options, so you can, for example, revoke your Mobiil-ID if you lose your phone, and still use the your main ID card to sign things.
Is the app tied to Google or Apple?
(Though Smart-ID is its own thing and is a fair bit more locked down, but I’ve managed to get it running on a phone without Google services IIRC.)
But, like the parent said, you have many other options other than the physical ID-card as well. Most people these days use Mobiil-ID or SmartID, which works on your phone and even smart watch. SmartID is completely free and Mobiil-ID is tied to your phones carrier, so the cost varies, but it's a one-time set-up fee of around 5€. Mobiil-ID certificate also lasts 5 years.
(When will people learn that biometrics are not another factor: they're entirely public and irrevocable. It's not just security theater, but Apple & Google know that this forces you into their ecosystem, which should be illegal. Of course, Brussels is full of rubes anyway.)
"a device could be used as evidence of possession, provided that there is a ‘reliable means to confirm possession through the generation or receipt of a dynamic validation element on the device’"
So in essence the TOTP has to be bound to the device in a way that prevents users from just extracting the secret and putting in in their password manager. Hypothetically that would still allow Yubikeys and other security keys that provide attestation from the factory, but in practise banks probably don't want to deal with the support headache and just provide their own, like the TAN generator mentioned by other commentors.
Two other highlights from the interpretation of the EBA:
"App installed on the device" -> not sufficient/compliant
"In the case of an SMS, and as highlighted in Q&A 4039, the possession element ‘would not be the SMS itself, but rather, typically, the SIM-card associated with the respective mobile number’."
"SIM-card associated with the mobile number" - is that even technically possible? Do mobile carriers provide a API for banks to verify that a number still corresponds to the same SIM card? If so I've never heard of it.
[0] https://web.archive.org/web/20191207213213/https://eba.europ...
When confirming a large transfer, you also need to enter the payment amount in the device, and I assume this gets hashed into the number as well.
More recently (last 3/4 years), you can also use their mobile app to do this instead / as well as.
It can be SMS. As said in another comment, the main banks in Spain offer this authentication method while being PSD2 compliant. Some also offer a card with coordinates. So it's not mandatory in any way to use a banking app.
But yes banking apps are not mandatory, and likely won't be in the near future either, though the alternatives are treated a bit like second class citizens.
Edit to add this anecdote. My bank told me I need to use their app because SMS is not secure, but you need to activate their app using an SMS code!