I saw a tweet that said (paraphrasing): "In the future people won't have accounts. The person (and their wallet) will be the account." While I appreciate the sentiment, I think reality is much more nuanced than that because identity management is about relationships, not identities (whatever those are).
Supporting a relationship requires that we recognize, remember, and react to another party (person, business, or thing). In self-sovereign identity (SSI), the tools that support that are wallets and agents. For people, these will be personal. For a business or other organization they'll be enterprise wallets and agents. The primary difference between these is that enterprise wallets and agents will be integrated with the other systems that the business uses to support the relationships they have at scale.
Remembering and reacting to another entity requires that you keep information about them for the length of the relationship. Some relationships, like the one I form with the convenience store clerk when I buy a candy bar, are ephemeral, lasting only for the length of the transaction. I don't remember much while its happening and forget it as soon as it's done. Others are long-lasting and I remember a great deal in order for the relationship to have utility.
So, let's say that we're living in the future where SSI is ubiquitous and I have a DID-based relationship with Netflix. I have a wallet full of credentials. In order for my relationship to have utility, they will have to remember a lot about me, like what I've watched, what devices I used, and so on. They will likely still need to store a form of payment since it's a subscription. I call that an account. And for the service Netflix provides, it's likely not optional.
Let's consider a different use case: ecommerce. I go to a site, select what I want to buy, supply information about shipping and payment, and submit the order. I can still create a DID-based relationship, but the information needed from me beyond what I want to buy can all come from my credentials. And it's easy enough to provide that I don't mind supplying it every time. The ecommerce site doesn't need to store any of it. They may still offer to let me create an account, but it's optional. No more required than the loyalty program my local supermarket offers. The relationship I create to make the purchase can be ephemeral if that's what I want.
What will definitely go away is the use of accounts for social login. In social login, large identity providers have accounts that are then used by relying parties to authenticate people. Note that authentication is about recognizing. SSI wallets do away with that need by providing the means for different parties to easily create relationships directly and then use verifiable credentials to know things about the other with certainty. Both parties can mutually authenticate the other. But even here, social login is usually a secondary purpose for the account. I have an account with Google. Even if I never use it for logging in anywhere but Google, I'll still have an account for the primary reasons I use Google.
Another thing that goes away is logging in to your account. You'll still be authenticated, but that will fade into the background as the processes we use for recognizing people (FIDO and SSI) become less intrusive and fade into the background. We have a feel for this now with apps on our smartphones. We rarely authenticate because the app does that and then relies on the smartphone to protect the app from use by unauthorized people. FIDO and SSI let us provide similar experiences on the web as well. Because we won't be logging into them, the idea of accounts will fade from people's consciousness even if they still exist.
I don't think accounts are going away anytime soon simply because they are a necessary part of the relationship I have with many businesses. I want them to remember me and react to me in the context of the interactions we've had in the past. SSI offers new ways of supporting relationships, especially ephemeral ones, that means companies need to store less. But for long-term relationships, your wallet can't be the account. The other party needs their own means of remembering you and they will do that using tools that look just like an account.