The most important secrets are the most mundane to the public: the location and capability of military assets, such as nuclear missiles. Maybe technologies under R&D, such as aircraft, intelligence gathering techniques, or cryptography techniques are at the next level down.

The loss of these secrets would seriously weaken the U.S. in diplomacy since adversaries would know the exact limits and shortfalls in U.S. military power.

Most secrets, as you rightly assume, aren't in this class. Most of them are analysis literally gleaned from the open internet and combined in a report to a policy maker.

I don't think the classification system is a good repository for secret corruption. Tenured federal employees have little reason to hide the impropriety of an elected official; on the contrary, they can get a cash bonus for reporting the malfeasance! In the rare cases when corruption was masked by military secrets, e.g. the Iran Contra affair, the profits were small (in the tens of thousands) compared to the scale of the wrongdoing (the undermining of the rule of law, Congress, and the people).

The best way to detect corruption would be to have better aggregation of officials' assets and analysts dedicated to the task. Elected officials and security clearance holders currently fill out an annual financial disclosure, but corruption can easily be obscured from the process.