A physical wallet is for carrying around money, credit cards, identification, membership cards, etc. In the same way, your digital wallet carries all the things you own on chain. It could just as easily be called a backpack or inventory of digital items.
A username and password represents who you are online--your digital identity. In the same way, your wallet proves who you are on blockchain and connects you to the history of everything you've done on chain. The wallet analogy fails to capture this aspect of what a wallet is. Passport might be a better analogy, but then that would miss the inventory aspect.
The core concept then is the ability to portably prove who you are, what you've done, and what you have.
So why is it that wallet UIs today focus so heavily on how much money is in your wallet? It's worth knowing, but it's hardly the whole story.
Consider the experience for empty wallets: the net worth is zero, so making that the largest piece of information is just depressing. If the wallet is brand new, there's no history of activity to show either.
New wallets need to focus on the identity aspect and only show history and assets as they are accrued.
Since the majority of new users would then be exposed to that basic experience, the emphasis on net worth would be a strange diversion from the norm if not handled well through the user journey.
P.S. bonus points if the brand new wallet helps the user through what they can do with a quest log.