Well yeah, in order for them to check your credit history they need to have been given prior access to the freeze or you need to temporarily thaw your freeze.
You should really have your credit frozen all the time to be honest.
Bigger question is, why is ‘having a good credit history’ a requirement for being eligible for health insurance?
(And the answer to that, of course, is that the ACA is first and foremost about the financial health of the insurers, and only incidentally about providing people with insurance, which in practice is mostly worthless for many/most people anyway, given the insane “deductibles”, premiums, and given that figuring out which doctors and which procedures (in which hospitals) are contracted is nigh-impossible by design, greatly reducing the ACA’s utility for actual human beings.)
Insurance is just a form of legal gambling, and the insurers make profit off of selling risk.
… which is precisely why a ‘medicare’-type solution (where access to health care is neither framed as a privilege, nor dependent on your having bought a ticket) is an categorically better approach. There’s really no reason why the system should be organized through insurers apart from path dependence / entrenched interests (including hospitals and doctors) and big money being behind the maintenance of this status quo.