Backing data that's strong enough to satisfy some critics is impossible to obtain.

Anecdotes? Obviously not OK.

Small-scale controlled experiments can be dismissed as nothing more than pointless toy exercises that have no bearing on real-world production code.

Large-scale controlled experiments are impractical. Blinding and placebos aren't possible. Isolating confounding elements such as individual performance would be difficult.

Burden of proof is burdensome, I guess.

Basically yes. I'm sure it would be possible to do a good study but very expensive. Although if the potential upside is increasing the productivity of an entire industry maybe it's worth doing.