And many many don't. It's not a requirement to have a passport or driving license to open a bank account, or to sign up with a credit agency (although many/most lenders will want some ID to actually lend to you).
I don't have a british passport, a british drivers license, but I do have a NI number. I can vote, I can open bank accounts, I can get amazon parcels, I can do normal daily things without them. The only people who have my NI number are 1) the electoral register, 2) my employer, and 3) hmrc (as far as I'm aware at least).
I've not shared it with Amazon (who are the company mentioned in the post), or with my utility provider, or with my broadband provider. I've also not given them my passport or drivers licence, and yet they all seem perfectly capable of verifying I am who I say I am, all without me having any form of national ID.