The problem IMO is not this particular case, but the concept itself of your credit history having anything to do with access to healthcare and the precedent that it sets.
Credit history should indeed be credit history. It should not be used for anything else. Using it a primary identity verification method is flawed for a variety of reasons. Proving your identity and being part of the UK banking system are two different things (foreigners visiting the UK have no reason to open any financial/credit accounts here, and yet still need to be able to prove their identity, and this is just one of many examples). Furthermore CRAs aren’t really reputed for their customer service and you wouldn’t want your access to healthcare depending on everything being alright with the CRA.
There’s also the privacy aspect of it - you might not want CRAs to know that you requested a Covid test considering these companies also provide marketing/data broker services and one of them was recently told off by the ICO so it isn’t even just a theoretical concern.