That doesn't solve the whole problem. Identity is fundamentally about what you are. What you have, or what you know, are merely proxies, and they need to be connected to you in a trusted way, which is hard to do in a robust and efficient way.
Or, in other words, when you misplace your private key, you don't want to irrecoverably lose everything you have. Fortunately, the world isn't some nightmarish cryptocurrency dystopia - there are ways to prove you owned the lost credentials and keep the ownership of what you had. The flip side of it is that someone else can prove they own your stuff too, with enough effort.
It solves the problem of having to give the company enough information for them to steal your identity in order to do business with them. That isn't a power companies should have over you, and those who do should be extremely heavily regulated to ensure their data protection is top level quality.
This way it isn't a big deal if small businesses leak data, since they don't have the important parts, so they don't need to be regulated that hard.
Or, in other words, when you misplace your private key, you don't want to irrecoverably lose everything you have. Fortunately, the world isn't some nightmarish cryptocurrency dystopia - there are ways to prove you owned the lost credentials and keep the ownership of what you had. The flip side of it is that someone else can prove they own your stuff too, with enough effort.