The cost saving question always comes up, and it’s true that in the (very) long term there are savings to be had by not duplicating information every which way and having multiple systems to access it. The big problem in the short to medium term is that what you currently having is massive duplication of information accessed by multiple systems, and somehow you need to convert it into the format that covers everything that everyone needs and is accessible by everyone. That’s the bit that costs a fortune.
The archetypal example of this is the attempt to unify the NHS’ record keeping system into one national healthcare record, which started about 20 years ago, cost at least £10 billion pounds (maybe double that?) and didn’t work and had to be abandoned in 2013. They’re finally making some headway on some systems of this kind some 20 years later, but still nothing close to the scale they had intended. This is why people are sceptical of the government’s intention to unify umpteen systems into this national ID card.