Game theoretically, unless there is a process to certify that a state
is not a good-faith signatory, then this zero-cost non-compliance
renders the conventions moot.
This is an upside down way to think about it. The premise that violating the Geneva Conventions is "zero-cost non-compliance" is false. A declaration that a country is not a good-faith signatory is not a sanction recognized under international law nor is it one that makes any sense. But that doesn't mean that a country doesn't face any consequences for violating international law.
If a country is a signatory of the Geneva Conventions, then a violation of the Geneva Conventions by the signatory, or by people who are the responsibility of the signatory, is wrongful. And, such a wrongful act is, for diplomatic purposes, a violation of international law. A violation of international law may provide a legal or political basis for another country, or authorities in the violating country (perhaps following a regime change), to punish citizens of the country who carry out the violations, or to punish the country itself.
Punishments might include international economic sanctions, arms embargoes, discontinuance of diplomatic relations, travel bans, war crimes trials of participants after the fact (some countries claim universal jurisdiction over all war criminals even if their country had not involvement in the actions), providing military or economic aid to the party on the other side of the conflict with a violator, or even proportionate military intervention to prevent violations of the Geneva Conventions from continuing.
Sanctions for violating the Geneva Convention are meted out unilaterally by other countries, can be imposed by the legal system of the violating country, or can be imposed by an ad hoc group of other countries working together. International law is rarely enforced by some neutral, extra-national judicial body. Instead, international law is a justification for other countries to take action that might otherwise defy international norms in their treatment of another country or people affiliated with it. Put another way, international law primarily provides political justification for other countries to take action.
This justification is undermined if a country is a not a signatory of the Geneva Conventions (or is declared not to be one because it signed them in "bad-faith"). In that case, violations of the Geneva Conventions are not wrongful simply because they are violations of the Geneva Conventions. Instead, they would be subject only to any "customary international law" that is deemed to apply to all countries without regard to the treaties that it has signed, which would provide a less definitive basis for punishing or condemning violations of conduct that would violate the Geneva Conventions. Customary international law overlaps with the Geneva Conventions, but the Geneva Conventions has many provisions that clarify where lines are drawn between acceptable and unacceptable conduct that are more specific than customary international law would be.
The Geneva Conventions would never be made more effective by invalidating the assent of a country to them on the basis that they are made in bad faith. This would undermine the authority of the international community to condemn or punish the wrongful actor.
Furthermore, more generally, international law, unlike the private law of contracts between natural persons or legally recognized entities, does not recognize concepts such as the invalidation of a treaty obligation by virtue of duress or bad-faith (although a good faith mistake of fact that makes the matter agreed to non-sensical or does not reflect the intent of the parties is recognized).
To reverse the question, what benefit does a nation receive from being a "good faith signatory"? The question assumes that there is such a benefit by assuming that being declared a "bad faith signatory" would somehow harm a country. The notion that being a signatory is valuable primarily because it induces other countries to act in reliance on the signatory state's compliance is not a good model of how the Geneva Convention is supposed to work.