Without a comprehensive test program in which a number of props are tested to failure, there would be no way to tell whether this prop was suitable for use in its shortened condition.
Isn't the bolded part how they determined the limits in the first place?
No. A propeller vibration survey does not test to failure. They strain gauge the prop and look for operating conditions with large strains. Large strain = high vibration amplitude. It's just bending repeated many times per second.
...or whether a shortened condition was not tested at all.
Ahh, the conspiracy theory of forced propeller retirement
Let's note a point about old props not yet considered.
First, aluminum has a memory. It remembers every fatigue cycle, and they add up. There is no knee in the S-N curve (strain vs cycles), so add up enough cycles and the aluminum
will fracture. As the strains get larger the required number of cycles becomes less. It's like money in the bank. You can make a lot of little withdrawals or a few bigger ones, but eventually the account is empty.
Second, when a particular engine-propeller combination is certified with a prohibited operating range, it means the prop survey found large strains when run at that particular setting. Many of the prohibitions are "pass-through", i.e. you're not allowed run continuously within that range, but you can go up or down through it.
Here's the thing....as a subsequent operator, you have no way to know how often the prop was run through the prohibited range, or how quickly. You don't even know if the previous operators bothered to observe the prohibited range. Think it doesn't happen? Consider how many operators right here on VAF consider propeller vibration as something which can be dismissed.
So, there you are with an old prop. All you can do is a crack check, which only tells you it has not fractured
yet. It does not tell you how many cycles remain until failure.
Me? I like to start with a full bank account.