You hit uppon an important difference between the US and most of Europe/the UK. An system for tracking who your citizens are. In the Netherlands, where I live, the municipalities cooperate to keep track of all citizens, and their address (or lack thereof). This means that you never need to convince any beaurocrat that your identity exists. You might need to authenticate that you are indeed who you claim to be, but that is normally trivial (Show government photo id).
This simplifies the process massively.
The UK should not be included in here. There is no official national system for keeping track of citizens and municipalities barely cooperate. This means you have to keep proving your address for things like an opening a bank account.
This is due to a historical political issue and repeal of a national identification system, see also https://en.wikipedia.org/wiki/Identity_Cards_Act_2006.