Central government would typically be a customer

This is a wrong assumption, it's not that they aren't customers as they'll deal with hundreds of vendors/partners and will benefit from these changes regardless but national cyber & supporting IT agencies (including the UK) are often providers themselves to both other government agencies and private organizations in the country.

This can be anything from running their SOC functions to specialized consulting services to intelligence sharing so the bill is definitely relevant and the exclusion of the govt. doesn't seem to serve a purpose other than saving the budget to implement/maintain their own rules.