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The problems are that:
when this central database is compromised - which it inevitably will be - all of the connected services are compromised at the same time.
Currently identity theft requires tediously working from weaker to stronger proofs of identity, which takes time, effort, money and increases opportunities for detection. With a centralised DB you just need to compromise a single disgruntled DBA and harvest all the bulletproof IDs you want.
various illiberal policies in the past have been hampered or limited by the lack of such a system.
Presumably there are objectionable policies the government either passed but couldn't enforce, or would have passed if it were practicable, which will be back on the menu. Delegating immigration enforcement to landlords is bad enough - imagine the Home Office had access to all this data for p-hacking plausible excuses for their tabloid-friendly xenophobia.
Again, it's not the actual piece of plastic I am advocating for, forget that. Like @Lolo describes you can build a very sophisticated system without the card itself.
It's the central database and the digital identities I am in favour of, and when you killed off the cards you pretty much killed off the opportunity to build the database.