Insurer admits wife is covered under policy, but does not want to cover claims since wife does not have authority to sign deceased husband's name to an insurance check for repairs.
It's not that they don't want to cover it. At least that shouldn't be the reason.
If she was not a Named Insured and was just defined as "an insured" then she has no rights to the policy or it's benefits. It's the Named Insured's estate
that has the rights.
If the claim rep has decided that the claims are legit and payable he would be wise to just make out the checks "To the Estate of Mr Named Insured" and send them to the surviving spouse and be done with it.
You can explain to her that she needs to open probate and get court papers appointing her as representative of the estate. Once she has them she can act on behalf of the estate, deposit the settlement checks in the estate account and, once probate is over, she can distribute the money to herself.
That's how it works.
Although it's possible that the insurance company's policy is to get the court papers before issuing the checks to the estate. That's OK, too.