This is literally how it works in majority of the real world; except for things where government has a role to play; most common case is taxes. If you are a landlord and collect rent from tenant and if either of you want to make tax related claims to the government, then you will have to provide/quote each other's government recognized identity in your tax returns.
For large parts of the population in the lower socio-economic strata, even this won't be relevant. And that reliance on that web-of-trust is the problem for them due to class discrimination etc. Hence, having a government issued identity (as a universal right) which acts as an anchor to which trusted attestations can be attached to is critical to make a difference in the life of the last person in that socio-economic line.
This is in essence the basis for India's identity system Aadhaar[1] – which is super minimal identity system – just biometrics (fingerprint, iris scan, head/shoulder photo, gender) – mapped to a a 12 digit number (basically a unique key in its database); plus 3 additional demographic fields – name, age (date of birth), address – which require external anchor proofs (which are very weak proofs). Here's the full list of accepted proofs - https://uidai.gov.in/images/commdoc/valid_documents_list.pdf