Yes, governments do need a centralized common identity if they intend to build something like a social credit system. Those without adequate experience dealing with the US system, for instance, may assume that the government already has your info and thus such a system is redundant. However, this is simply not the case. US government systems are a hodgepodge of different systems built by different vendors, over different computing eras, many of which lack a primary key relationship with something like your social security number (the current “default” identifier). Many are plagued with duplicate records, data problems, and other issues that prevent easy correlation of records without human verification. Talk to some people in the IRS or Social Security and you’ll quickly get a sense of how many problems this can create! Maybe it’s improved since I last talked to people about it, but I doubt it.
A central ID enforced on all systems by statute would significantly reduce the barrier to creating “airtight” oppressive systems. While the inefficiencies in the US system have a cost, certainly preventing the implementation of more efficient social benefit programs, they also provide a barrier against more efficient social repression. Given the political animosity present in the country right now, it’s probably good that we don’t have the ability to create a turnkey totalitarian system. Things are bad enough as is!
More generally, in nations where the population feels suspicion towards their politicians and bureaucrats, the people may prefer to leave inefficiencies baked into the system in order to hamper potential oppression. Those social tensions and trust deficits should be resolved before proceeding with any ambitious central ID schemes.