Why regulators care, and what they actually regulate. State insurance law does not approve reinsurance contracts. It regulates whether the ceding insurer may take credit for one. The NAIC's Credit for Reinsurance Model Law opens: "Credit for reinsurance shall be allowed a domestic ceding insurer as either an asset or a reduction from liability on account of reinsurance ceded only when the reinsurer meets the requirements of Subsections A, B, C, D, E, F or G of this section." That single sentence is the whole regulatory hinge. An insurer that has ceded risk still holds reserves against the policies it issued; taking credit is what lets it reduce those reserves, and reduced reserves are what free up capital to write new business. The simplest route to credit, in Subsection A, is that "the reinsurance is ceded to an assuming insurer that is licensed to transact insurance or reinsurance in this state," with further routes for accredited, trusteed and certified reinsurers and for those domiciled in reciprocal jurisdictions.
The model law states its own purpose as protecting "the interest of insureds, claimants, ceding insurers, assuming insurers and the public generally," and it declares an intent "to ensure adequate regulation of insurers and reinsurers and adequate protection for those to whom they owe obligations." The protection it provides to a policyholder is therefore indirect and worth naming as such: the rules exist so that an insurer cannot reduce the reserves standing behind your policy by ceding risk to a counterparty that cannot pay.
Credit is not the same as coverage, and the state guaranty association system says so expressly. The NAIC's Life and Health Insurance Guaranty Association Model Act lists among the things the act "shall not provide coverage for" a "policy or contract of reinsurance, unless assumption certificates have been issued pursuant to the reinsurance policy or contract." An assumption certificate is the document by which the reinsurer takes over the original insurer's obligation directly to the policyholder, which converts an arrangement between two companies into a promise to the individual. Absent one, the guaranty association is protecting the policy your insurer issued, not the reinsurance behind it, and the distinction only becomes visible at insolvency.
The vocabulary tells you which side of the trade a filing is describing. The same transaction is ceded reinsurance on the buyer's books and assumed reinsurance on the seller's, which the NAIC glossary carries as its own entry: "the assumption of risk from another insurance entity within a reinsurance agreement or treaty." Authorized reinsurance is "reinsurance placed with a reinsurer who is licensed or otherwise allowed to conduct reinsurance within a state," which is the same idea as credit approached from the reinsurer's side.
The capacity point is the reason the market exists. A single insurer's ability to write a large or concentrated exposure is limited by its own surplus. Ceding part of that exposure, and being allowed to take credit for it, lets the insurer stand behind more coverage than its own balance sheet could support alone, which is how coverage exists at all for risks larger than any one company would accept. That is also the honest limit of the arrangement: the capacity it creates is real, and the counterparty risk it creates is a genuine exposure the regulator supervises rather than eliminates.