On one hand the risk of ending up in a "papers, please" situation is not to be underestimated.
On the other hand, this is not the 1960s anymore. We do not live in an isolated utopia where we proud Brits never need to show any documents, like our pesky European cousins do.
We need to prove citizenship or right to live and work here every time we rent a property or start a new job.
In theory, passports are not compulsory; in practice, good luck proving citizenship without a passport. Driving licences (which not everyone has) and national insurance number do not prove citizenship.
Those who think ID cards are an overreach should think that it was precisely the absence of ID cards which allowed the Windrush scandal, ie the deportation of people who had every right to be here, including some who were citizens, but who lacked the documents to prove it. That scandal could NOT have happened in Spain France Germany Italy etc, precisely because they have ID cards. Food for thought.
Part of the problem with the Windrush scandal was that the Home Office had come up with capricious requirements which most Brits would have been unable to meet, like providing multiple proofs of address for each year going back decades. I think that's a worse overreach than an ID card system. But to each their own. Convincing Brits of the merits of ID cards is like convincing Texans about the soundness of gun control laws :)