Earlier quoted context omitted.
That's not the case in the UK - we don't have any single government issued identity document/card that everyone has to have.
The UK is a special case and will not be "Europe" for long besides. Homogenisation of rules can take a while, especially when there is a cultural aversion to them. In this case I'd say there simply has not been enough time for this to happen.
The EU was never comparable to, say, America in terms of unity. Europe had too much history for it to work perfectly - every one was on what had been at some point some one else's land.
[0] https://europedirectemn.files.wordpress.com/2018/02/treaties...