You will have all your email, postal addresses, other PII and (formerly physical) identification documents in a wallet app. Government websites AND private websites will be able to request data from that wallet for login and registration purposes. You will need to approve all requests to your wallet, in the majority of cases by using biometrics (e.g. faceId or non-apple alternatives of it).
This has the potential to eradicate several major avenues of fraud. The more of this is offered (for free) by governments the more it could majorly disrupt (=destroy) the industry around the topic.
Worldwide it seems there is a new, proprietary wallet each month, which naturally totally ruins this idea of having one wallet, but I see what is currently going on as a "storming phase" or almost "norming phase" already, that will eventually reach the "performing phase", with one or two wallets being the survivors. A big stumbling block here is that everyone involved wants a piece of the cake.
The European Union is actively (but slowly) working on this, e.g. with eIDAS. With eIDAS, you create a digital identity in your home country. If that home country DI offering supports eIDAS, you can use it to login to any other government AND private service implementing any DI offering that supports eIDAS.
> whether identity providers / VC providers are going to be 5 big firms
The big firms will provide the ecosystem (e.g. Microsoft Entra, mastercard-id-for-rp, ...), the real identity verification will happen through offerings like Onfido, Jumio and the 1000 other offerings in the space.