I agree we might be at the point of trading anecdotes. I would suggest though that there could be the problem that a team works hard to produce good outputs
in spite of Scrum, rather than
because of it.
My feeling, as I have mentioned elsewhere is that this burden of proof is on Scrum and Scrum proponents to back up the claim that it facilitates better business outcomes than would otherwise have been obtained without Scrum.
The reason I think it's fair that Scrum has the burden of proof is that it is so far-reaching and overbearing in its degree of prescripting exactly the manner of working.
Scrum as a system is responsible for micromanaged enforcement of exactly one set of meetings, exactly one cadence of work, special new positions with Scrum-specific job duties, constraints on team structure, like cross-functionality and minimizing specialization, that there must be some form of aggregateable workload estimation, etc., all which are part and parcel with every Scrum implementation I've heard of (meaning that whether all these prescriptions are explicitly listed in some Scrum manifesto or not, they are absolutely a part of Scrum).
Given all this costly overhead and one-size-fits-all prescription, I think it's very fair to say, "prove it." If I know that my team works really well in our own ad hoc way that is tailored to our specializations, our current workload, our preferences, the way we jell as a team, etc., then why should I agree this other way is definitely, empirically going to be better?
I'm not saying any other team should use the custom methods my team has found to be productive. But why would we need to give them up for a system nobody has proven to be better, and many people have argued to be worse?