You could put an endless series of unique identities on the BIP 32 tree structure. Its personal identity management we are talking about here. This is identity freedom. Identity empowerment.
For regular world "credit rating" you would need to consolidate everything into one identity though. There's just no way around that. One social security number / tax identification number / social insurance number / driver's license number / passport number. If you're a normal average person who would go through a normal average life, you need to stick to one identity for your home, your credit, your car and any loans from a normal bank.
Yep this is already the world we live in. But right now its very hard to live an alternative lifestyle, trezor would make living the alternative lifestyle more possible. Additionally it would vastly improve your security if you did decide to go the mainstream route. And its use would have massive external benefits mostly realized in the form of lower prices for goods and services for previously mentioned reasons.
Really using the identity that was attached to your real physical person would just afford you a deeper line of credit at a lower interest rate. Simply because it would make creditors more comfortable to know they could find and badger the real you if you failed to fulfill. You are always going to get a better interest rate if you expose your real person, but plenty of people would get good interest rates without doing that im sure.