A blockchain funded and controlled by a central authority or group is just a slow and unnecessarily complex database --- wholly built around trust and easily implemented to better effect with less effort/cost by traditional means.
No, not really. A blockchain without a native currency is imparted no special economic security i.e. insurmountable costs to rewrite data.
If you want a system that allows anyone to participate and secure high stakes transactions, you cannot allow cheap revisionism or censorship which is exactly what traditional systems allow (through power or bribes). A blockchain without a native currency is void of any economic security.
I'm not sure what you believe the "gotcha" is when your hypothetical removes the most crucial aspect in order to try and prove the tech is useless.
A blockchain with authoritative access has marginal use: it can reduce trust (but not realistically defend against economic attacks) - it certainly pales in comparison to the societal application of a network which is robust while allowing arbitrary participation in consensus.
People, skeptics included, get stuck on the word blockchain and build arguments stating that any data structure which is a cryptographic chain of hashes is the true subject of interest. Blockchain doesn't offer the compelling parts of "crypto" anymore than a care without an engine offers the ability to drive.
Economic (or game theoretic, if you like) defense against converging power is the primary draw. It is why technologically minded people so often don't truly grok it - because the cryptography is (important) implementation details. It is the incentives which emerges from those schemes that is primarily important.
I don't need to prove anything that the marketplace hasn't already.
The burden of proof is on anyone proposing a blockchain solution --- which I assumed is what you were looking to address.
One can reason about fundamentals more competently than the average market participant. Isn't that the point of this community? Venture capital adjacent folk who profit off of being more well informed than the market.