I live, now, in a country with ID cards. These are not actually compulsory; but everyone has got one and it is according to an international standard. It means I can cross any borders, enter most countries (even non-EU ones) without fuss (getting into UK is quicker than using my UK passport!). I can do everything without ever having to produce copies of a recent gas bill (except when dealing with UK insurance companies). I have never, ever been asked to show it by a policeman. I am only ever asked under the same circumstances as UK people ask for identification. I have done certain jobs in two countries (including England) where I was required to carry, at all times, an identity card. I survived.
Last year, I wanted to take an internal flight, in England, from Manchester. They demanded a form of identity with my photograph. A driving licence was not acceptable. I was given no notice. Fortunately I had my identity card. I asked what they would do if not, answer: then you can not fiy. I visited my English bank: I proved my identity with the magic photo. card. My children all used to carry passports when they went out as the only way of proving their ages to enter clubs, buy drink and so on. This was expensive. They wore out the standard passports in no time.
You live in a country where they photograph you non-stop, where if a DNA sample is taken for any reason it is retained for years, where rather trivial, everyday transactions expect you to carry photographic proof of who you are. You live in a country that refused to join Schengen, while accepting more non-European immigrants than the rest put together, so you have to show passports even for a day trip to France. (I just walk across the border, never asked most of the time. If so, I've got this tiny card, if I remember to put it in my wallet). You do not trust politicians, whom you elect and can throw out; but you happily sign up to Google or Facebook and trust a commercial company, whose living is advertising, that is foreign owned and so beyond the law, not to misuse the information. You let credit companies keep the most outrageous details, true and false.
Get over it: persuade the government to produce a functional card that does not try to carry your whole life on a chip and use it to reduce the daily bother and restore some of the freedom of movement that you once had.
Do n't bleat about not trusting politicians. You elected them; you joined their parties or ignored their antics. Get off your bottoms and take part in democracy at every level. Tell commercial entities to take a running jump when they demand photocopies of a recent bank statement or bill (to me these are more personal than anything on my identity card). Stop complaining about illegal immigrants if you are not prepared for even the most basic means of identifying them (not that it really stops them).
GB is one of the most watched, controlled, surveilled countries in the world. Get one, basic form of identity and fight the "informal", all pervasive stuff to show yuo have proved who you are.
I do wonder, did you all refuse to get birth certificates for your children? Death certificates for the deceased? National Insurance numbers?
As for cost: you are the electorate. You've got directly elected MPs and councillors. Sort it out.