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There's no inherent law that says a voltage mode circuit with no blocking cap will saturate. But proving it won't requires analyzing every aspect of the circuit which contributes, and this should be done for all operating conditions (line, load, temperature, component tolerance, etc). It turns out to be an extremely involved exercise, as opposed to adding a capacitor or a current control loop.

Peak current mode control is a simple innter/outer control scheme. At least I'm not aware of a simpler one.

Testing with a single prototype is absolutely not sufficient.