Don
Because you'd end up with duplicated data, out dated data, and missing data.
The whole idea of a census is that it gives an accurate snapshot of the population at a specific time so you shouldn't be getting Mr Smith counted twice because two different systems have him down slightly differently, or you end up having to try and work out which data from which system is actually correct at the specific time which is a mammoth task.
Also a lot of the other systems have highly sensitive information on them, so you ideally never link them together more than you absolutely need to for data protection reasons...
To give an idea, my brother in law found he wasn't registered at his GP, apparently he'd not been for long enough they'd removed him, whilst there are accounts of people who've died still being on a GP's register years later because the GP hadn't been informed.
HRMC is usually working at least a month, sometimes up to a year out of date, the hospital records don't necessarily show where you are living at the moment or at all if you've not needed a hospital visit for a number of years so the hospital and your GP might have different records neither of which may be correct for where you actually are.
It's also worth remembering that many government systems don't ask where you are living, just where you can be contacted because people like students might be living at one end of the country but still going "home" to the parents over the holidays.
The Census gets all sorts of information together in a fairly cheap way, probably far cheaper than linking the other systems, let alone linking them securely and then working out what data is accurate when you've got conflicting information, and gets information you don't necessarily get on the other systems - I'm not sure which government system would actually know everyone's specific job, HMRC might know your income but that doesn't help with things like working out if certain jobs are increasing, decreasing, disappeared or are new (and if need be work out if support is needed to keep skills alive).
Exactly, just because there's data "all over the place" doesn't mean that this data is tied together - because ultimately it's pretty much impossible to do. You don't own your data, you don't have absolute rights over the data, the data is linked to you but ultimately it's also potentially linked to others, or owned by other people - you have a FB account - the data on there you fill in, is stored in their identity repository; Facebook likely owns that data, and also has links to that data. There's a lot of people, clever people trying to figure out the data question currently - look into OIDC, OpenBanking, FAPI to gain an understanding of it.
There is no central Identity repository. There's no one place which stores all your data and chances are, there won't ever be. Lots of reasons why (such as anonymity online); But based on the Zero sum structure which laws are based on - states you can't both own a piece of land, or a piece of property, but with data that's different and the issue is building rights around that; Think of data as copyright information. Artists have an economic right to that copyright - music can be copied many times and the value of the music doesn't diminish. Data can be copied, shared and it's value also doesn't diminish. Data is maintained at the authoritive source - meaning if you have a gmail account, or FB account, or your records held by the government, updates are made directly at that point.
For there to be on central database of information you'd have to lose anonymity when signing up for services - if you sign up to gmail, you'd have to provide a central ID which allows the data to be linked back to you. If you sign up to Amazon, the same. Also, there's existing data and how to deal with that, you probably already have a gmail account - would you then be expected to prove who you are, or lose access to this? It's a mine field.
Linking together the information (government, GP, NHS etc) is all well and good - but there's questions which come from linking that data - who controls and owns the data? Who picks through the data to ensure it's all the same across multiple sources? How can you prove who you are, based on that data? You can't, as the model for all of this data was turned upside down when the internet became popular. But there was never one set of data held for you - the Government has data, your employer has data, your wife or children has data on you and a lot of this might differ - you expose data based on the audience which you want to see it; There's now 1000's of identity providers out there who hold a copy of your data (or a subset of it) and it'll be impossible for all identity providers to come together to link it all together and keep one record of it - as you'd have to have a single corporation which essentially has taken over the world.
Any ways, bit of a rant and probably a conversation for a thread by itself.